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 will substitute the value of y from the second equation into the first equation and solve for x.
First, substitute y=-4x-1 into the first equation:
1/2x - 5(-4x-1) = 5
Simplify the equation by distributing the -5 to both terms inside the parentheses:
1/2x + 20x + 5 = 5
Combine like terms on the left side of the equation:
20.5x + 5 = 5
Subtract 5 from both sides of the equation:
20.5x = 0
Divide both sides of the equation by 20.5:
x = 0
Now we have found the value of x. Next, substitute this value into the second equation to find y:
y = -4(0) - 1
y = -1
Therefore, the solution to the system of linear equations is x = 0 and y = -1.