Question

How do you solve `x-3y=4` and `-3x+5y=-14` using substitution?

Answer 1

`y=0.5`
`x=5.5`

Explanation:

First, we rearrange one of the formulae to give us `x` in terms of `y` (or vice versa)
`x-3y = 4" "` (Add `3y` to both sides)
`x = 4+3y`

Now we can substitute in our value for `x` into the other equation so that we only have one unknown, `y`.

Then you expand the bracket and simplify it to find `y`.

`-3x + 5y = -14`
`-3 (4+3y) + 5y = -14`

(expand the brackets)

`-12 - 9y +5y = -14`

(simplify the `y` terms)

`-12-4y = -14`

(add `12` to both sides)

`-4y=-2`

(divide both sides by `-4` to isolate the `y` term)

`y=-2/-4`
`y = 0.5`

We then substitute the `y` value into the original equation to find `x` (you can use either of the equations for this)

`x=4+3y`
`x=4 +(3xx0.5)`
`x=4 + 1.5`
`x=5.5`

Then we can use the other equation to check our answer.

`-3x+5y=-14`
`-(3xx5.5) + (5xx0.5) = -14`
`-16.5+ 2.5=-14`
`-14 = -14`
So we know our answer is right!