10x - 2y = -4 ==== (1)
4x + 5y = -19 ==== (2)
To solve the system we should make the coefficients of y have the same values to eliminate it, then
Multiply equation (1) by 5 and equation (2) by 2
5(10x) - 5(2y) = 5(-4)
50x - 10y = -20 ===== (3)
2(4x) + 2(5y) = 2(-19)
8x + 10y = -38 ===== (4)
Now add equations (3) and (4) to eliminate y
(50x+8x) + (-10y + 10y) = (-20 + -38)
58x + 0 = -58
58x = -58
Divide both sides by 58 to find x
x = -1
Substitute the value of x in equation (1) or (2) to find the value of y
4(-1) + 5y = -19
-4 + 5y = -19
Add 4 to both sides
-4 + 4 + 5y = -19 + 4
0 + 5y = -15
5y = -15
Divide both sides by 5 to find y
y = -3
The solution of the system is (-1, -3)
