Solve each system of linear equation and explain any method you used:
5x+4y=-1
-7x-2y=-13
To solve this system of linear equations, we can use the method of substitution.
First, we solve one equation for one variable and substitute it into the other equation.
From the first equation, we can solve for x:
5x + 4y = -1
5x = -4y - 1
x = (-4y - 1)/5
Now we substitute this value of x into the second equation:
-7x - 2y = -13
-7((-4y - 1)/5) - 2y = -13
(28y + 7)/5 - 2y = -13
28y + 7 - 10y = -65
18y = -72
y = -72/18
y = -4
Now that we have the value of y, we can substitute it back into the expression for x:
x = (-4y - 1)/5
x = (-4(-4) - 1)/5
x = (16 - 1)/5
x = 15/5
x = 3
Therefore, the solution to the system of linear equations is x = 3 and y = -4.