The given system of equations is expressed as
-10x - 10y = 10
-2x - 5y = -19
The first step is to make the coefficients of one of the variables in each equation equal. To make the coefficient of x equal, we would multiply the first equation by 2 and the second equation by 10. It becomes
- 20x - 20y = 20 equation 3
- 20x - 50y = - 190 equation 4
We would eliminate x by subtracting equation 4 from equation 3. It becomes
- 20x - - 20x - 20y - - 50y = 20 - - 190
- 20x + 20x - 20y + 50y = 210
30y = 210
y = 210/30
y = 7
Substituting y = 7 into the second equation, it becomes
- 2x - 5 * 7 = - 19
- 2x - 35 = - 19
- 2x = - 19 + 35 = 16
x = 16/- 2
x = - 8
The solution is
(- 8, - 7)