Which is the value of y in the system of equations 4x-5y=18 5x+y=58

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