Solve each system of linear equation and explain any method you used:
5x+4y=-1
-7x-2y=-13
To solve this system of equations, we will use the substitution method.
1) Begin by isolating one variable in the first equation. Let's choose to isolate x:
5x + 4y = -1
5x = -4y - 1
x = (-4y - 1)/5
2) Substitute this expression for x into the second equation:
-7((-4y - 1)/5) - 2y = -13
(-28y - 7)/5 - 2y = -13
(-28y - 7 - 10y)/5 = -13
-38y - 7 = -65
-38y = -65 + 7
-38y = -58
y = -58/-38
y = 29/19
3) Substitute the value of y back into the expression for x:
x = (-4(29/19) - 1)/5
x = (-116/19 - 19/19)/5
x = (-135/19)/5
x = -135/19 * 1/5
x = -135/95
Therefore, the solution to the system of equations is x = -135/95 and y = 29/19.