Question

How do you solve `4x+y=-5` and `2x+3y=5` using substitution?

Answer 1

`x=-2`
`y=3`

Explanation:

`4x+y=-5`
`2x+3y=5`

Rearrange the first equation for `y`:

`4x+y=-5`

`y=-5-4x`

Substitute `y` into second equation and solve for `x`:

`2x+3y=5`

`2x+3(-5-4x)=5`

`2x-15-12x=5`

`2x-12x=5+15`

`-10x=20`

`x=20/-10`

`x=-2`

Then substitute the value of `x` into one of the original equations to find the solution for `y`:

`4x+y=-5`

`4(-2)+y=-5`

`-8+y=-5`

`y=-5+8`

`y=3`

Double check your solution by substituting values of `x=-2` and `y=3` into any of the original equations and see whether you get the numerical solution (`-5` or `5`).