{3x+y=-9
{-3x+-2y=12
What is the y-value of the solution to this system of equations?
A. -7
B. -3
C. -2
D. -1
I tried them all and I must have did something wrong because none of them worked. Help please!! Thanks.
To find the y-value of the solution to this system of equations, you can solve the given equations simultaneously to obtain the values of x and y. Let's go through the steps together:
Step 1: Start by multiplying the first equation by 2 to make the coefficient of y the same in both equations, and make it easier to eliminate y.
2*(3x + y) = 2*(-9)
6x + 2y = -18 ----> Equation 1'
-3x - 2y = 12 ----> Equation 2
Step 2: Add equation 1' and equation 2 together to cancel out the variable y.
(6x + 2y) + (-3x - 2y) = -18 + 12
Combine like terms:
6x + (-3x) + 2y + (-2y) = -6
Simplify:
3x = -6
Step 3: Solve for x by dividing both sides of the equation by 3.
3x / 3 = -6 / 3
x = -2
Step 4: Substitute the value of x (-2) into either of the original equations to find the y-value.
Using the first equation:
3*(-2) + y = -9
Multiply:
-6 + y = -9
Step 5: Solve for y by adding 6 to both sides.
-6 + 6 + y = -9 + 6
y = -3
Therefore, the solution to the system of equations is x = -2 and y = -3.
Now, let's check the answer choices provided:
A. -7: Not the solution since y = -3
B. -3: The correct solution!
C. -2: Not the solution since y = -3
D. -1: Not the solution since y = -3
So, the correct y-value of the solution to this system of equations is -3, which corresponds to answer choice B.