Problem: Solve the following system of equations
6x-5y=-12
5x-9y=-10
1) 6x - 5y = -12
2) 5x - 9y = -10
Multiply equation 1 by 9.
9(6x - 5y) = -12 * 9
3) 54x - 45y = -108
Multiply equation 2 by 5.
5(5x - 9y) = -10 * 5
4) 25x - 45y = -50
Subtract equation 4 from equation 3.
54x - 45y = -108
-(25x - 45y = -50)
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29x = -58
29x = -58
29x/29 = -58/29
x = -2
Substitute that into equation 1 to solve for y.
6x - 5y = -12
6(-2) - 5y = -12
-12 - 5y = -12
-12 - 5y + 12 = -12 + 12
-5y = 0
-5y/-5 = 0/-5
y = 0
Use equation 2 to verify.
5x - 9y = -10
5(-2) - 9(0) = -10
-10 - 0 = -10
-10 = -10
Answer: x = -2, y = 0