Final answer:
To solve the system of equations, we can use the method of substitution. Solving one equation for one variable and substituting the expression into the other equation, we find that x = -7/3 and y = -1.
Step-by-step explanation:
To solve the system of equations, we can use the method of substitution. We start by solving one equation for one variable and then substitute that expression into the other equation. For example, we can solve the first equation for x:
3x + 5y = -12
3x = -12 - 5y
x = (-12 - 5y) / 3
Now, we substitute this expression for x into the second equation:
12((-12 - 5y) / 3) + 2y = 6
Simplifying this equation gives us:
-12 - 20y + 2y = 6
Combining like terms:
-12 - 18y = 6
Adding 12 to both sides:
-18y = 18
Dividing both sides by -18:
y = -1
Substituting this value of y into either of the original equations:
3x + 5(-1) = -12
3x - 5 = -12
3x = -7
x = -7/3
So, the solution to the system of equations is x = -7/3 and y = -1.