The solution to the system of equations is x = -4 and y = 0, obtained through the substitution method, where the first equation is solved for y and the result is substituted into the second equation.
In the given example, the substitution method was employed to solve a system of two equations:
Start with the system of equations:
y = -x - 4
3x - 5y = -12
Solve the first equation for y:
y = -x - 4
Substitute this expression into the second equation:
3x - 5(-x - 4) = -12
Simplify the expression:
3x + 5x + 20 = -12
Combine like terms:
8x + 20 = -12
Isolate x:
8x = -32
x = -4
Substitute x = -4 into the first equation and solve for y:
y = -(-4) - 4
y = 4 - 4
y = 0
Therefore, the solution to the system of equations is x = -4 and y = 0.