What is the value of y in the solution set of the system of linear equations shown below?
y=-x+12
4x-2y=36
A. 10
B. 8
C. 6
D. 2***
I think its D but Im not sure, help?
Thank you!
To find the value of y in the solution set of the system of linear equations, we can substitute the value of y from the first equation into the second equation.
Given equations:
y = -x + 12 ----(1)
4x - 2y = 36 ----(2)
Substituting the value of y from equation (1) into equation (2), we get:
4x - 2(-x + 12) = 36
Simplifying equation (2):
4x + 2x - 24 = 36
6x - 24 = 36
Adding 24 to both sides of the equation:
6x - 24 + 24 = 36 + 24
6x = 60
Dividing both sides of the equation by 6:
6x / 6 = 60 / 6
x = 10
Now, we can substitute the value of x back into equation (1) to find y:
y = -x + 12
y = -10 + 12
y = 2
Therefore, the value of y in the solution set of the system of linear equations is 2, so the correct answer is D.
To solve the system of linear equations, you can use substitution or elimination method. Let's use the substitution method to find the value of y.
Given equations:
1) y = -x + 12
2) 4x - 2y = 36
Step 1: Solve the first equation for y.
Since the equation 1) is already solved for y, we have y = -x + 12.
Step 2: Substitute the value of y (from equation 1)) into the second equation.
Substitute -x + 12 for y in equation 2):
4x - 2(-x + 12) = 36
Step 3: Simplify the equation.
4x + 2x - 24 = 36
6x - 24 = 36
Step 4: Isolate the variable x.
Add 24 to both sides of the equation:
6x - 24 + 24 = 36 + 24
6x = 60
Step 5: Solve for x.
Divide both sides of the equation by 6:
6x/6 = 60/6
x = 10
Step 6: Substitute the value of x into equation 1) to find y.
Substitute x = 10 into y = -x + 12:
y = -(10) + 12
y = -10 + 12
y = 2
Therefore, the value of y in the solution set of the system of linear equations is 2. The correct answer is D) 2.
4 x - 2 (-x+12) = 36
4x + 2x -24 = 36
6 x = 60
x = 10
y = -10+12 = 2 sure enough