Solve each system of linear equation and explain any method you used:
-1/2x-5y=5
y=-4x-1
To solve this system of linear equations, we can use substitution method.
First, let's rewrite the second equation in terms of x:
y = -4x - 1
Now, substitute this expression for y in the first equation:
-1/2x - 5(-4x - 1) = 5
Simplify the equation:
-1/2x + 20x + 5 = 5
Combine like terms:
39/2x + 5 = 5
Subtract 5 from both sides:
39/2x = 0
Multiply both sides by 2/39 to isolate x:
x = 0
Now, substitute this value of x back into the second equation to find y:
y = -4(0) - 1
y = -1
Thus, the solution to the system of linear equations is x = 0 and y = -1.