Final answer:
To solve the given system of linear equations by substitution, we first solve one of the equations for y and then substitute it into the other equation to find x. After finding x, we substitute it back to find y. The solution is x = -2 and y = 2.
Step-by-step explanation:
To solve the system of equations by substitution, we start with the given equations:
-7x + 2y = 18
6x + 6y = 0
First, we solve the second equation for y:
6x + 6y = 0
6y = -6x
y = -x
Next, we substitute y = -x into the first equation:
-7x + 2(-x) = 18
-7x - 2x = 18
-9x = 18
x = -2
Now we substitute x back into y = -x to find y:
y = -(-2)
y = 2
Therefore, the solution to the system of equations is x = -2 and y = 2.