Question

How do you solve `x+5y=-3` and `3x-2y=8` using substitution?

Answer 1

See the entire simplification process below:

Explanation:

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

`x + 5y = -3`

`x + 5y - color(red)(5y) = -3 - color(red)(5y)`

`x + 0 = -3 - 5y`

`x = -3 - 5y`

Step 2) Substitute `-3 - 5y` for `x` in the second equation and solve for `y`:

`3x - 2y = 8` becomes:

`3(-3 - 5y) - 2y = 8`

`(3 xx -3) - (3 xx 5y) - 2y = 8`

`-9 - 15y - 2y = 8`

`-9 - 17y = 8`

`color(red)(9) - 9 - 17y = color(red)(9) + 8`

`0 - 17y = 17`

`-17y = 17`

`(-17y)/color(red)(-17) = 17/color(red)(-17)`

`(color(red)(cancel(color(black)(-17)))y)/cancel(color(red)(-17)) = -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 = -3 - 5y` becomes:

`x = -3 - (5 xx -1)`

`x = -3 - (-5)`

`x = -3 + 5`

`x = 2`

The solution is: `x = 2` and `y = -1` or `(2, -1)`