Question

How do you solve `4x-3y = -15` and `x + y = 5` using substitution?

Answer 1

`x = 0; " "y = 5`

Explanation:

Given:
`4x -3y = -15color(white)(..................)A`
`x +y = 5color(white)(............................)B`

Then, from equation B:
`color(blue)(x = 5 - y)`

Substitute for `x` in equation A;
`4color(blue)((5 - y)) -3y = -15`
`20 - 4y -3y = -15`
`20 -7y = -15`
`-7y = -15 -20" "` multiply both sides by `-1`
`7y = 35`
`y = 5`

Substitute the value of `y` in equation B:
`x +y = 5`
`x +5 =5`
`x = 5 - 5`
`x = 0`

To check, substitute the values into equation A":
`4x -3y = -15`
`4(0) -3(5) = - 15`
`-15 = -15`