Multiple Choice For the following system of equations, what is the x-value of the solution? –x + 2y = 6 6y = x + 18 (1 point) Responses –18 –18 0 0 –6 –6 3
The given system of equations is:
-x + 2y = 6
6y = x + 18
To find the x-value of the solution, we can solve the system of equations by eliminating one variable.
First, let's multiply the second equation by -1:
-x + 2y = 6
-6y = -x - 18
Now, let's add the two equations together:
-x + 2y = 6
+ -x - 6y = -18
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-8y = -12
Dividing both sides of the equation by -8, we have:
y = 12/8
y = 3/2
Now, let's substitute this value of y back into one of the original equations, such as the first one:
-x + 2(3/2) = 6
-x + 3 = 6
-x = 6 - 3
-x = 3
Dividing both sides of the equation by -1, we have:
x = -3
Therefore, the x-value of the solution is -3.