Using systems of equations, we need to eliminate one variable to make it into a 1 variable equation either using elimination or substitution.
Equation 1: 4x - 5y = 18
Equation 2: 5x+y = 58
For equation 2, there is only one y which makes it easy to substitute. So subtract 5x from both sides of the equation to get
y = -5x+58
Then we know what y is in terms of x, so plug it into equation 1.
4x - 5(-5x+58) = 18
It is now an equation with only 1 variable, which we can solve.
Distribute the -5 to (-5x+58)
4x+25x-290 = 18
Combine like terms
29x-290 = 18
Add 290 to both sides
29x = 308
Divide both sides by 29 to isolate the x
x = 308/29 wow what an ugly number, but its alright
Plug in x to equation 2 to find what y is
5(308/29)+y = 58
1540/29+y = 58
Subtract 1540/29 from both sides
y = 142/29
The y value is 142/29
