Question

How do you solve the system of equations `4x + y = 15` and `7x - 2y = 15` by the substitution method?

Answer 1

`x =3" "y=3`

Explanation:

`4x +color(red)(y) =15" and " 7x -2y =15`

There is a single `color(red)(y)` in the first equation.

Re-arrange it to find `y` in terms of `x`.

`color(red)(y =(15-4x))`

Replace `color(red)(y)` in the second equation with `(color(red)(15-4x))`

`color(white)(................................................)7x - 2color(red)(y)=15`
`color(white)(........................................................)color(red)(darr)`
`color(white)(.........................................)7x - 2(color(red)(15-4x))=15`

`color(white)(...............................................)7x -30+8x=15`

`color(white)(...............................................................)15x=45`
`color(white)(..................................................................)color(blue)(x=3)`

Now that you know the value for `x`, find the value for `y`.

`y=15-4color(blue)(x)`

`y=15-4color(blue)((3))`

`y = 15-12`
`y =3`