To solve this system of equations, we can use the method of substitution or elimination.
Let's use the method of elimination:
First, we will multiply both sides of the first equation by 3 and the second equation by 2 to make the coefficients of x equal:
-6x + 2y = -32 (multiply by 3)
4x + 3y = -9 (multiply by 2)
Simplifying, we have:
-18x + 6y = -96
8x + 6y = -18
We can now subtract the second equation from the first equation:
-18x + 6y - (8x + 6y) = -96 - (-18)
Simplifying further, we have:
-18x + 6y - 8x - 6y = -96 + 18
-26x = -78
Dividing both sides of the equation by -26, we have:
x = -78 / -26
x = 3
Now, we can substitute the value of x into one of the original equations to solve for y. Let's use the first equation:
-6(3) + 2y = -32
Simplifying, we have:
-18 + 2y = -32
Adding 18 to both sides of the equation, we have:
2y = -14
Dividing both sides of the equation by 2, we have:
y = -14 / 2
y = -7
Therefore, the solution to the system of equations is x = 3 and y = -7.
-6x + 2y = -32
4x + 3y = -9
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