Question

How do you solve by substitution `x - 4y = -1` and `3x + 5y = 31`?

Answer 1

`x=7`
`y=2`

Explanation:

We are given:

`x-4y=-1`

and

`3x+5y=31`

We can do this a number of ways, but let's start with `x-4y=-1`

Let's multiply `x-4y=-1` by `-3` to get its `x` to look like the `x` in `3x+5y=31` but with an opposite sign:

`x-4y=-1`

`(-3)(x-4y)=(-3)(-1)`

`-3x+12y=3`

Now, let's add `-3x+12y=3` to `3x+5y=31` to get rid of those `x`'s:

`-3x+12y=3`
`3x+5y=31`

`17y=34`

Now, divide both sides by `17` to get:

`y=2`

Now, just plug in the value for `y` into `3x+5y=31`

`3x+5y=31`
`3x+5(2)=31`
`3x+10=31`

subtract both sides by `10`:

`3x+10=31`
`3x=21`

divide both sides by `3`:

`3x=21`
`x=7`

So, `x=7` and `y=2`

To check if our answers are correct, you can take either of the two given equations and plug in the values of `x` and `y`.

Let's try this with `x-4y=-1`

`x-4y=-1`

`(7)-4(2)=-1`

`7-8=-1`

`-1=-1`