We can use substitution to solve this system of equations. We can solve the first equation for y and get:
y = (2x + 12)/3
We can then substitute this expression for y into the second equation:
(2x + 12)/3 + 3x = -7
Multiplying both sides of this equation by 3 to eliminate the denominator, we get:
2x + 12 + 9x = -21
Simplifying this equation gives:
11x = -33
Dividing both sides by 11, we get:
x = -3
We can then substitute this value of x back into either of the two original equations to find y. Using the first equation, we get:
3y = 2(-3) + 12
3y = 6
y = 2
Therefore, the solution to the system of equations is x = -3 and y = 2.
To check the solution, we substitute these values back into both equations:
3y = 2x + 12 3(2) = 2(-3) + 12 6 = 6
This equation is true, so the solution (x = -3, y = 2) checks out.