Solve the system of equations.−6x+2y=−32 4x+3y=−9
To solve the system of equations:
-6x + 2y = -32 (Equation 1)
4x + 3y = -9 (Equation 2)
We can use the method of elimination. Multiply Equation 1 by 2 and Equation 2 by 3 to make the coefficient of "y" in both equations the same:
-12x + 4y = -64 (Equation 3)
12x + 9y = -27 (Equation 4)
Add Equations 3 and 4 together:
-12x + 4y + 12x + 9y = -64 - 27
13y = -91
Divide both sides by 13:
y = -7
Substitute this value of y back into Equation 1:
-6x + 2(-7) = -32
-6x - 14 = -32
-6x = -32 + 14
-6x = -18
x = 3
The solution to the system of equations is x = 3 and y = -7.