Question

How do you solve `y-2x=3` and `2x-3y=21` using substitution?

Answer 1

`x=-7.5`
`y=-12`

Explanation:

Start by writing one of these 2 equations in terms of `x` or `y` so that you have a substitutable form. Note that the substitutable means in the form of "`x=`" or "`y=`"

I'm going to start with getting `y-2x=3` in terms of `y`. I will call this equation 1. All we have to do here is add `2x` to each side,

`y-2x=3`
Adding `2x` to each side:
`y=3+2x`

Now that we have the equation in terms of `y`, we can substitute this term (3+2x) into the other equation (equation 2).

`2x-3y=2x-3(3+2x) =21`

Notice that now we have one equation with one variable. This means we can go ahead and solve for `x`

`2x-3(3+2x)=2x-9-6x=-4x-9=21`
Adding 9 to both sides,
`-4x=21+9=30`
`x=-7.5`

Now that we have a value for `x`, we can substitute back into equation 1 to solve for `y`.

`y-2x=y-2(-7.5)=y+15=3`
Subtracting 15 from both sides and this solving for y,
`y=3-15=-12`

Therefore,
`x=-7.5`
`y=-12`