Question

How do you solve the system `x+4y=8` and `2x-5y=29` using substitution?

Answer 1

See the entire solution process below:

Explanation:

Step 1) Solve the first equation for `x`:

`x + 4y - color(red)(4y) = 8 - color(red)(4y)`

`x + 0 = 8 - 4y`

`x = 8 - 4y`

Step 2) Substitute `8 - 4y` for `x` in the second equation and solve for `y`:

`2x - 5y = 29` becomes:

`2(8 - 4y) - 5y = 29`

`(2 xx 8) - (2xx4y) - 5y = 29`

`16 - 8y - 5y = 29`

`16 - 13y = 29`

`-color(red)(16) + 16 - 13y = -color(red)(16) + 29`

`0 - 13y = 13`

`-13y = 13`

`(-13y)/color(red)(-13) = 13/color(red)(-13)`

`(color(red)(cancel(color(black)(-13)))y)/cancel(color(red)(-13)) = -1`

`y = -1`

Step 3) Substitute `-1` for `y` in the solution to the first equation at the end of Step 1 and calculate `x`:

`x = 8 - 4y` becomes:

`x = 8 - (4 xx -1)`

`x = 8 - (-4)`

`x = 8 + 4`

`x = 12`

The solution is `x = 12` and `y = -1` or `(12, -1)`