What is the general form of the equation of a circle with center at (a, b) and radius of length m? A. X2 y2 − 2ax − 2by (a2 b2 − m2) = 0 B. X2 y2 2ax 2by (a2 b2 − m2) = 0 C. X2 y2 − 2ax − 2by (a b − m2) = 0 D. X2 y2 2ax 2by a2 b2 = -m2.
Answers
The general form of the equation of a circle with center at (a, b) and radius of length m is written as \((x-a)^2+(y-b)^2 = m^2\).
What is the general form of the equation of a circle?The general form of the equation of a circle is written as,
\((x-h)^2+(y-k)^2 = R^2\)
where (h, k) is the coordinates of the center of the circle, while R is the radius of the circle.
Equation of circle with center at (a, b) and radius of length mWe have already discussed the general form of the equation of a circle, substituting the values into it,
\((x-h)^2+(y-k)^2 = R^2\\\\(x-a)^2+(y-b)^2 = m^2\)
Hence, the general form of the equation of a circle with center at (a, b) and radius of length m is written as \((x-a)^2+(y-b)^2 = m^2\).
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Related Questions
a group fo seven kids line up in a random order. each ordering of the kids is equally likely. there are three girls and four boys in the group
Answers
The total number of possible orders of the group is 7!. However, we need to take into account that each ordering is equally likely.
In a group of seven kids with three girls and four boys, the probability of a random order has to be found out.
To determine the total number of possible orders, we use the concept of permutations. The total number of ways to arrange seven kids is 7 factorial, denoted as 7!.
Since there are three girls and four boys, we can determine the number of ways to arrange them separately. The number of ways to arrange three girls is 3 factorial (3!). Similarly, the number of ways to arrange four boys is 4 factorial (4!).
To find the probability of a random order, we divide the number of favorable outcomes (which is 7!) by the total number of possible outcomes.
Hence, the probability of a random order is 1, as there is only one possible order among the 7!
In conclusion, a group of seven kids lining up in a random order will result in only one possible order.
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Graph each system and determine the number of solutions that it has. If it has one solution, name it. I only need help with B.
Answers
1 solution: (-1,-3)
1) Since we are going to solve these systems graphically, let's begin by setting one pair of t-tables:
b) 2x-y=1, y=-3
2x-y=1 ⇒-y= 1 -2x ⇒ y=2x-1
Now, let's plot those points and trace one increasing line for the first one, and one horizontal line for the constant function y=-3
2) Plotting that system, we can tell the solution is the common point to both equations:
Thus, the answer is (-1,-3)
the number of hours worked per year per person in a state is normally distributed with a standard deviation of 39. a sample of 15 people is selected at random, and the number of hours worked per year per person is given below. calculate the 98% confidence interval for the mean hours worked per year in this state. round your answers to the nearest integer and use ascending order. time 2051 2061 2162 2167 2169 2171 2180 2183 2186 2195 2196 2198 2205 2210 2211 provide your answer below:
Answers
Using a t-distribution with 14 degrees of freedom (n-1) and a 98% confidence level (α = 0.02/2 = 0.01 for each tail), we have:
sample mean (x) = (2051+2061+2162+2167+2169+2171+2180+2183+2186+2195+2196+2198+2205+2210+2211)/15 = 2180.6
sample standard deviation (s) = 39
standard error of the mean (SEM) = s/√n = 39/√15 ≈ 10.077
t-score for a 98% confidence level and 14 degrees of freedom (from t-distribution table or calculator) = 2.977
Margin of error (ME) = t-score × SEM = 2.977 × 10.077 ≈ 30.05
Therefore, the 98% confidence interval for the mean hours worked per year in this state is:
(x- ME, x+ ME) = (2180.6 - 30.05, 2180.6 + 30.05) = (2150, 2211)
Rounding to the nearest integer and putting the limits in ascending order, we get:
(2150, 2211)
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An algorithm is a calculation that determines how long it will take to solve a problem. True or False?
Answers
The given statement "An algorithm is a calculation that determines how long it will take to solve a problem." is False.
An algorithm is not just a calculation that determines how long it will take to solve a problem. An algorithm is a step-by-step set of instructions or a process used to solve a problem or perform a specific task. It is a systematic approach that allows a computer or human to break down a problem into smaller, manageable parts and reach a solution effectively.
Algorithms are the foundation of computer programming and can be applied in various fields such as mathematics, data processing, and problem-solving. They can be simple, like finding the largest number in a list, or complex, like solving a Rubik's Cube.
Efficiency is a key factor in evaluating algorithms. The time and resources required for an algorithm to solve a problem can vary greatly depending on the method used. However, the primary purpose of an algorithm is to provide a clear and concise procedure to reach a solution, rather than just estimating the time needed to solve a problem.
In summary, an algorithm is a well-defined process designed to perform a specific task or solve a problem, rather than just calculating the time required to do so. Its effectiveness depends on its efficiency, accuracy, and the simplicity of the steps involved.
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A manufacturer of household kettles subjected 50 kettles to 10 000 hours of testing. Test results for the 50 kettles show that there were two failures at 3500 hours, two failures at 4800 hours, one failure at 8600 hours, and two more failures at 9000 hours.
4.1.1 Calculate the failure rate percentage (FR %).
4.1.2 Calculate the number of failures per unit-hour (FR N).
4.1.3 Calculate the MTBF at this point in testing.
Answers
Answer:
4.1.1 The failure rate percentage (FR%) is 14%.
4.1.2 The number of failures per unit-hour (FR N) is 0.0007 failures per hour.
4.1.3 The MTBF at this point in testing is 6,928.57 hours.
Given that:
Manufacturer of household kettles subjected 50 kettles to 10,000 hours of testing.
4.1.1 Test results for the 50 kettles show that there were two failures at 3500 hours, two failures at 4800 hours, one failure at 8600 hours, and two more failures at 9000 hours.
Therefore,
FR% = (Total number of failures / Total number of items tested) * 100
Putting values,
FR% = (7 / 50) * 100FR%
= 14%
Therefore, the failure rate percentage (FR%) is 14%.
4.1.2 Number of Failures per Unit-Hour (FR N)
The number of failures per unit-hour (FR N) is calculated as the total number of failures divided by the total number of hours tested.
Therefore,
FR N = Total number of failures / Total number of hours tested
Putting values,
FR N = 7 / 10,000FR N
= 0.0007 failures per hour
Therefore, the number of failures per unit-hour (FR N) is 0.0007 failures per hour.
4.1.3 Mean Time Between Failures (MTBF)
The Mean Time Between Failures (MTBF) is the average time between the failures.
The formula for MTBF is:
MTBF = Total hours of operation / Total number of failures
Therefore,
MTBF = (3,500 × 2) + (4,800 × 2) + (8,600) + (9,000 × 2) / 7MTBF
= 48,500 / 7MTBF
= 6,928.57 hours
Therefore, the MTBF at this point in testing is 6,928.57 hours.
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Algebra 1, P.3 Geometric sequences HD
Type the missing number in this sequence:
-3,
-6,
-12, 24,
-48,
Answers
what fraction is equivalent to 4/16
Answers
Answer:
1/4
Step-by-step explanation:
4/16=2/8=1/4
Answer:
1/4
Step-by-step explanation:
4/16 = 1/4 (divide the numerator and denominator by the same number. In this case, 4)
3:
Lloyd has a bag of 3 marbles. There is 1 orange marble, 1 green marble, and 1 blue marble.
List 1 List 2 List 3 List 4
O O, O O, O O, O
G O, G O, G O, G
B O, B O, B O, B
G, O G, O G, O
G, B G, B G, B
G, G G, G G, G
B, B B, B B, B
B, G B, G B, G
B, O B, O
G, O
O, B
G, B
Which list gives the sample space for pulling 2 marbles from the bag with replacement?
List 1
List 2
List 3
List 4
Answers
List 4 provides space for the sample to remove 2 marbles from the bag and replace them.
What is sample?In statistics and probability, a sample is a subset of a population that is selected for observation, analysis, or testing. The population refers to the entire group of individuals, objects, or events that share a common characteristic of interest, while the sample is a smaller group that is selected to represent the population.
According to question:List 4 provides space for the sample to remove 2 marbles from the bag and replace them.
Each element in List 4 represents a possible outcome of selecting 2 marbles from the bag, where the order of selection matters and replacement is allowed. For example, the first element in List 4, "G, O", represents the outcome of first selecting a green marble, then replacing it in the bag, and then selecting an orange marble.
The other lists represent possible outcomes of selecting 2 marbles, but some of them do not allow for replacement or do not include all possible orderings. For instance, List 1 only includes outcomes where both marbles are the same color, while List 2 does not include all possible orderings (e.g., it does not include the outcome "O, G").
Therefore, List 4 is the correct answer as it represents the sample space for selecting 2 marbles from the bag with replacement and includes all possible outcomes.
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Answer:
List 4
Step-by-step explanation:
List 4 provides space for the sample to remove 2 marbles from the bag and replace them.
What is sample?
In statistics and probability, a sample is a subset of a population that is selected for observation, analysis, or testing. The population refers to the entire group of individuals, objects, or events that share a common characteristic of interest, while the sample is a smaller group that is selected to represent the population.
According to question:
List 4 provides space for the sample to remove 2 marbles from the bag and replace them.
Each element in List 4 represents a possible outcome of selecting 2 marbles from the bag, where the order of selection matters and replacement is allowed. For example, the first element in List 4, "G, O", represents the outcome of first selecting a green marble, then replacing it in the bag, and then selecting an orange marble.
The other lists represent possible outcomes of selecting 2 marbles, but some of them do not allow for replacement or do not include all possible orderings. For instance, List 1 only includes outcomes where both marbles are the same color, while List 2 does not include all possible orderings (e.g., it does not include the outcome "O, G").
Therefore, List 4 is the correct answer as it represents the sample space for selecting 2 marbles from the bag with replacement and includes all possible outcomes.
An answering service staffed with one operator takes phone calls from patients for a clinic after hours. Patient phone calls arrive at a rate of 15 per hour. The interarrival time of the arrival process can be approximated with an exponential distribution. Patient phone calls can be processed at a rate of u 25 per hour. The processing time for the patient phone calls can also be approximated with an exponential distribution. Determine the probability that the operator is idle, i.e., no patient call is waiting or being answered.
Answers
The probability that the operator is idle is 0.4, or 40%. This means that the operator is idle 40% of the time and is available to answer calls.
To determine the probability that the operator is idle, we need to use the M/M/1 queuing model, where M stands for Markovian or Memoryless arrival and service time distributions, and 1 stands for one server.
The arrival process can be modeled with an exponential distribution with a rate of λ = 15 calls per hour. The service time can also be modeled with an exponential distribution with a rate of µ = 25 calls per hour.
Using the M/M/1 queuing model, we can calculate the utilization factor ρ as follows:
ρ = λ / µ
ρ = 15 / 25
ρ = 0.6
The utilization factor ρ represents the percentage of time that the server is busy. Therefore, the probability that the operator is idle, i.e., no patient call is waiting or being answered, can be calculated as follows:
P(0 customers in the system) = 1 - ρ
P(0 customers in the system) = 1 - 0.6
P(0 customers in the system) = 0.4
Therefore, the probability that the operator is idle is 0.4, or 40%. This means that the operator is idle 40% of the time and is available to answer calls.
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Aubrey's dinner cost $85. She tips the waitstaff 30%% for excellent service How much does Aubrey tip the waitstaff?
Answers
Answer:
$25.50
Step-by-step explanation:
We need to find 30% of 85:
30%*85
Convert 30% to a fraction to make the math easier:
\(\frac{30}{100}*85=\frac{3}{10}*85=25.5\)
She tipped the waiter $25.50
Jack is standing on the ground talking on his mobile phone. He notices a plane flying at an altitude of
2400 metres. If the angle of elevation to the plane is 70° and by the end of his phone call it has an angle
of elevation of 50°, determine the distance the plane has flown during Jack’s phone call - use the cosine rule
Answers
Using the cosine rule, the distance the plane has flown during Jack's phone call can be calculated by taking the square root of the sum of the squares of the initial and final distances, minus twice their product, multiplied by the cosine of the angle difference.
To determine the distance the plane has flown during Jack's phone call, we can use the cosine rule in trigonometry.
The cosine rule relates the lengths of the sides of a triangle to the cosine of one of its angles.
Let's denote the initial distance from Jack to the plane as d1 and the final distance as d2.
We know that the altitude of the plane remains constant at 2400 meters.
According to the cosine rule:
\(d^2 = a^2 + b^2 - 2ab \times cos(C)\)
Where d is the side opposite to the angle C, and a and b are the other two sides of the triangle.
For the initial angle of elevation (70°), we have the equation:
\(d1^2 = (2400)^2 + a^2 - 2 \times 2400 \times a \timescos(70)\)
Similarly, for the final angle of elevation (50°), we have:
\(d2^2 = (2400)^2 + a^2 - 2 \times 2400 \times a \times cos(50)\)
To find the distance the plane has flown, we subtract the two equations:
\(d2^2 - d1^2 = 2 \times 2400 \times a \times (cos(70) - cos(50))\)
Now we can solve this equation to find the value of a, which represents the distance the plane has flown.
Finally, we calculate the square root of \(a^2\) to find the distance in meters.
It's important to note that the angle of elevation assumes a straight-line path for the plane's movement and does not account for any changes in altitude or course adjustments that might occur during the phone call.
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A monkey is born weighing 48 ounces at birth and after a year weighs 14 pounds. What is the monkey's growth rate per day? Round to the hundredths if needed. Note that there are 16 ounces in every 1 pound.
Answers
The monkey's growth rate per day rounded to the nearest hundredth is;
0.03 pounds per day
To solve this we need to convert first the monkey's weight at birth to pounds from ounces.Weight of monkey at birth = 48 ounces = 48/16 pounds = 3 poundsWeight of monkey a year after birth = 14 poundsNow, the difference in weight after a year = 14 - 3 = 11 pounds.There are 365 days in a year and therefore, the increase in weight per day will be;
Rate of increase in weight per day = 11/365 = 0.03 pounds per day
In conclusion, the monkey's growth per day = 0.03 pounds per day
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Which value of x makes the equation 3.5(x+20)=6+.75(x+1) true?
Answers
Answer:
x = -23
Step-by-step explanation:
3.5(x+20) = 6 + .75(x + 1) Multiply the terms inside the parentheses on the left by 3.5 and the parentheses on the left by .75
(3.5)x +(3.5)(20) = 6 + (.75)x +(.75)(1)
3.5x + 70 = 6 + .75x + .75 Combine the 6 and .75 on the right side
3.5x + 70 = 6.75 + .75x Subtract .75x from both sides of the equation
2.75x + 70 = 6.75 Subtract 70 from both sides of the equation
2.75x = -63.25 Divide both sides by 2.75
x = -23
Check
3.5(-23+20) = 6 + .75(-23 + 1)
3.5(-3) = 6 +.75(-22)
-10.5 = 6 +(-16.5)
-10.5 = -10.5
Answer:
x = -23
Step-by-step explanation:
3.5(x+20)=6+.75(x+1)
3.5x + 70 = 6 + .75x + .75
3.5x+70=.75x+6.75
2.75x+70=6.75
2.75=−63.25
divide^
x = -23
The system of equations shown is solved using the linear combination method
StartLayout 1st row 1st column 6 x minus 5 y = negative 8 right-arrow 2nd column 6 x minus 5 y = negative 8 right-arrow 6x minus 5 y = negative 8 2nd row 1st column negative 24 x + 20 y = 32 right-arrow one-fourth (negative 24 x + 20 y = 32) right-arrow negative 6 x + 5 y = 8 with Bar Underscript 3rd row 3rd column 0 = 0 EndLayout
What does 0 = 0 mean regarding the solution to the system?
Answers
The 0 = 0 in the solution to the system implies that the system of equations involving the equations 6x - 5y = -8 and 6x - 5y = -8 have infinitely many solutions
What are linear equations?
Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the linear combination to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
6x - 5y = -8
6x - 5y = -8
Subtract the equation 6x - 5y = -8 from the equation 6x - 5y = -8
6x - 5y = -8
- 6x - 5y = -8
----------------------
0 = 0
This in other words means that the difference between both equations is 0
When the solution to a system of equation is 0 = 0, it means that the system of equations have infinitely many solutions
Hence, the 0 = 0 in the solution to the system implies that the system of equations involving the equations 6x - 5y = -8 and 6x - 5y = -8 have infinitely many solutions
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Answer: The answer is D for those who don't like to read extra long expert answers (no offense to experts, just shorten answers to the direct answer pls)
Step-by-step explanation: Edge 2022
At noon the temperature was 12 degrees and went up throughout the day. If the temperature was no more than 36 degrees. How many degrees could the temperature have risen. Solve the inequality: 12 + x ≤ 36 *
Answers
Answer:
B
Step-by-step explanation:
Hope this helps :D
Use the inequality to help you complete the statements.
w > 4
The w in the inequality is the
The 4 in the inequality is the
Answers
The inequality w > 4 can be used to complete the following statements: The w in the inequality is the variable or unknown value being compared with the number 4. It represents an unknown quantity that is greater than 4.
The 4 in the inequality is the constant or known value that the variable w is being compared to. It is a number that is less than w.
Inequalities use mathematical symbols to compare two values and express their relationship.
In this case, the inequality w > 4 uses the symbol ">" which means "greater than." The inequality indicates that w is larger than 4, so any value of w that is greater than 4 will make the inequality true.
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solve by elimination
8x-14y=-6
12x-21y=5
Answers
Answer:
No solution
Step-by-step explanation:
\(8x - 14y = -6\\12x - 21y = 5\\\)
multiply both sides by -3
\(-24x + 42y = 18\\-24x - 42y = 10\\0 = 28\\\)
(eliminate the equations vertically to eliminate one variable )
the statement is false for any value of x and y therefore there is no solution to solve
I hope this helps!
Carmen has bought tickets for a raffle. The probability of her winning is 1/5What are the odds in favor of her winning
Answers
The probability of her winning is 1/5.
We have that odds in favor of a particular event are given by Number of favorable outcomes to Number of unfavorable outcomes. This is:
\(P=\frac{\text{favorable outcomes}}{unfavorable\text{outcomes}}\)Therefore, odds in favor of the winning is
\(1\colon4\)Answer: 1 : 4
Answer:
The probability is 20%.
Step-by-step explanation:
convert the fraction into percentage.
Howard University recorded an enrollment of 1060 freshman in 2019, which was a 13. 2% increase over the previous record in 2018. What was the freshman enrollment of 2018?
Answers
To find the freshman enrollment of 2018, we need to determine the original enrollment figure before the 13.2% increase.
Let's assume the freshman enrollment of 2018 is represented by "x."
According to the information given, the freshman enrollment in 2019 was a 13.2% increase over the previous record in 2018. This can be expressed as:
x + 0.132x = 1060
Combining like terms:
1.132x = 1060
Dividing both sides by 1.132:
x = 1060 / 1.132
x ≈ 937.26
Rounded to the nearest whole number, the freshman enrollment of 2018 at Howard University was approximately 937.
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Explain what's a greatest common factor. and solve this wander with explanation.
Answers
Answer:
4
Step-by-step explanation:
You just need to find the common factors, then find the largest in them.
help Which relation is a function?
Answers
Answer:
The answer is B
Step-by-step explanation:
an input value must only paired to one output value
-3(2d + 5) please help me solve this using distributive property
Answers
Answer:
-6d -15
Step-by-step explanation:
-3(2d + 5)
Distribute
-3 *2d -3*5
-6d -15
9x9x9= ?
okay, now they're gone...
whos down to talk?
Answers
Answer:
omgggg its been soooooooo long since weve talked how u been?
Step-by-step explanation:
Pls help me thank you <3
Solving by GCF
1)7x^2+2x=0
Solution(s) are is:
2)5b^2-10b=0
Solution(s) are is:
3)3d^2-d=0
Solution(s) are is:
4)17x^2+51x=0
Solution(s) are is:
Answers
Answer:
1. 9x³
2.5b³
3.2d
4. 68x³
9514 1404 393
Answer:
0, -2/70, 20, 1/30, -3Step-by-step explanation:
Factoring out the greatest common factor in each case, we can simplify the process of finding the non-zero solution. The solutions are the values of the variable that make the factors be zero.
1) 7x^2 +2x = 0 = (x)(7x +2) ⇒ x = 0; x = -2/7
__
2) 5b^2 -10b = 0 = (5b)(b -2) ⇒ b = 0; b = 2
__
3) 3d^2 -d = 0 = d(3d -1) ⇒ d = 0; d = 1/3
__
4) 17x^2 +51x = 0 = 17x(x +3) ⇒ x = 0; x = -3
There are 20 people trying out for a team. How many ways can you make randomly select for people to make a team?
Answers
There are 15,504 ways to randomly select a team of 5 people from a group of 20 people
If there are 20 people trying out for a team, the number of ways to select a team of n people can be calculated using the formula for combinations, which is:
C(20, n) = 20! / (n! * (20 - n)!)
where C(20, n) represents the number of ways to select n people from a group of 20 people.
For example, if we want to select a team of 5 people, we can plug in n = 5 and calculate:
C(20, 5) = 20! / (5! * (20 - 5)!) = 15,504
Therefore, there are 15,504 ways to randomly select a team of 5 people from a group of 20 people. Similarly, we can calculate the number of ways to select teams of different sizes by plugging different values of n into the formula for combinations.
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Item5 Time Remaining 57 minutes 22 seconds00:57:22 Item 5 Time Remaining 57 minutes 22 seconds00:57:22 Claire has had negative group experiences in college. She always seems to get stuck doing the bulk of the work, and her group members have always had terrible communication skills. Therefore, at work, when her boss proposes putting her on a task force, she is immediately apprehensive and fearful during the _____________ phase of socialization.
Answers
Claire experiences apprehension and fear during the anticipatory socialization phase of socialization when her boss proposes putting her on a task force at work, due to her negative group experiences in college.
Anticipatory socialization is the phase in the socialization process where individuals anticipate and prepare for their future roles and experiences in a particular social group or setting.
It involves forming expectations, attitudes, and behaviors based on past experiences and knowledge.
In Claire's case, her negative group experiences in college, where she often ended up doing most of the work and faced poor communication within the group, have shaped her expectations and attitudes towards group work.
As a result, when her boss proposes putting her on a task force at work, Claire immediately feels apprehensive and fearful.
She anticipates that she may face similar challenges, such as an uneven distribution of workload and ineffective communication, which could negatively impact her experience in the task force.
During the anticipatory socialization phase, individuals rely on their past experiences and perceptions to anticipate what they may encounter in a new social setting.
Claire's negative group experiences in college have influenced her apprehension and fear, as she expects the same difficulties to arise in the task force at work.
These emotions and concerns may impact her willingness to fully engage in the new group and could influence her interactions and behavior within the task force.
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1. How do I find the slope of (2,4) (4,7)
Answers
Answer: 3/2
Step-by-step explanation:
Rise over run!!!
Subtract y values, divide that by the subtracted x values.
7-4/4-2= 3/2
PLEASE HELP, WILL MARK BRAINlIEST
A circular flower bed is 23 m in diameter and has a circular sidewalk around it that is 3 m wide. Find the area of the sidewalk in square meters. Use 3. 14 for pi
Answers
The area of the sidewalk is 84.78 square meters if a circular flower bed is 23 m in diameter and has a 3 m wide circular sidewalk.
A circular flower bed is 23 m in diameter and has a circular sidewalk around it that is 3 m wide. The area of the sidewalk is square meters. The formula used: The area of the circle is given by:
πr²
Here, r = (d + 2w)/2, where d is the diameter and w is the width.
Substitute the values of d, w, and π in the above formula to get the area of the circular sidewalk.
Diameter of circular flower bed = 23 m
Width of circular sidewalk = 3 m
Radius of circular flower bed, r = (23+3)/2 = 13 m
Radius of circular sidewalk = (23+3+3)/2 = 14 m
Area of the circular sidewalk = π(14² - 13²) m²= π(14+13)(14-13) m²= 3.14(27) m²= 84.78 m²
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Find the integer that exceeds –5 by the same amount that 13 exceeds –1. \
Answers
Answer:
7
Step-by-step explanation:
13 exceeds - 1 by - 1 + 13 = 12, then
- 5 + 12 = 7
Answer:
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
13 exceeds - 1 by - 1 + 13 = 12, then
- 5 + 12 = 7
Use the elimination method to solve the system of equations. Choose the
correct ordered pair.
X+ y = 8
x- y = 6
A. (7,1)
B. (8,2)
C. (9,3)
D. (60)
Answers
Answer:
The answer is option A.
Step-by-step explanation:
The steps are :
\(x + y = 8 - - - (1)\)
\(x - y = 6 - - - (2)\)
\((1) - (2)\)
\(x + y - x - ( - y) = 8 - 6\)
\(2y = 2\)
\(y = 1\)
\(substitute \: y = 1 \: into \: (1)\)
\(x + 1 = 8\)
\(x = 7\)