Question

How do you solve the system of equations: 5x - 2y = 23 ; 5x + 2y = 17?

Answer 1

The solutions are
`color(blue)(x=4,y=-3/2`

Explanation:

`5x - color(blue)(2y) = 23`.........equation `(1)`
`5x + color(blue)(2y) = 17`.......equation `(2)`

Solving through elimination.
Adding the equations results in elimination of `color(blue)(2y`:
`5x - cancel(color(blue)(2y)) = 23`
`5x + cancel(color(blue)(2y)) = 17`

`10x=40`
`color(blue)(x=4`

Now finding `y` from equation `1`

`5x -2y = 23`

`5x - 23=2y`

`20-23=2y`
`-3=2y`

`color(blue)(y=-3/2`