Question

How do you solve `0.5x+0.25y=36` and `y+18=16x` using substitution?

Answer 1

`x = 5`
`y = 62`

Explanation:

In either equation, express one of the variables in terms of the other terms.

`[1] 0.5x + 0.25y = 36`
`[2] y + 18 = 16x`

If we solve for `y` in `[2]`, we have

`[3] => y = 16x - 18`

Now, substitute this relation into `[1]`

`[1] 0.5x + 0.25y = 36`

`=> 0.5x + 0.25(16x - 18) = 18`

Multiplying the entire equation by 4, we have

`=> 4(0.5x + 0.25(16x - 18) = 18)`

`=> 2x + 1(16x - 18) = 72`
`=> 2x + 16x - 18 = 72`

`=> 18x = 90`
`=> x = 5`

Using `[3]` (or `[1]` or `[2]`), solve for `y`

`y = 16x - 18`
`=> y = 16(5) - 18`

`=> y = 80 - 18`

`=> y = 62`