The solution is x = -4 and y = -8
Solution:
Given system of equations are:
x - 2y = 12 ------- eqn 1
5x + 3y = -44 --------- eqn 2
We have to solve the system of equations by elimination
Multiply eqn 1 by 3
3(x - 2y = 12)
3x - 6y = 36 -------- eqn 4
Multiply eqn 2 by 2
2(5x + 3y = -44)
10x + 6y = -88 ------------ eqn 5
Add eqn 4 and eqn 5
3x - 6y = 36
10x + 6y = -88
( + ) ----------------------
10x + 3x - 6y + 6y = 36 - 88
13x = 36 - 88
13x = -52
x = -4
Substitute x = -4 in eqn 1
-4 - 2y = 12
-2y = 12 + 4
-2y = 16
y = -8
Thus the solution is x = -4 and y = -8