Question

How do you solve the system `x-5y=36` and `2x+y=-16` using substitution?

Answer 1

See a solution process below:

Explanation:

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

`x - 5y = 36`

`x - 5y + color(red)(5y) = 36 + color(red)(5y)`

`x - 0 = 36 + 5y`

`x = 36 + 5y`

Step 2) Substitute `(36 + 5y)` for `x` in the second equation and solve for `y`:

`2x + y = -16` becomes:

`2(36 + 5y) + y = -16`

`(2 xx 36) + (2 xx 5y) + y = -16`

`72 + 10y + y = -16`

`72 + 10y + 1y = -16`

`72 + (10 + 1)y = -16`

`72 + 11y = -16`

`-color(red)(72) + 72 + 11y = -color(red)(72) - 16`

`0 + 11y = -88`

`11y = -88`

`(11y)/color(red)(11) = -88/color(red)(11)`

`(color(red)(cancel(color(black)(11)))y)/cancel(color(red)(11)) = -8`

`y = -8`

Step 3) Substitute `-8` for `y` in the solution to the first equation at the end of Step 1 and calculate `x`:

`x = 36 + 5y` becomes:

`x = 36 + (5 xx -8)`

`x = 36 + (-40)`

`x = -4`

The solution is: `x = -4` and `y = -8` or `(-4, -8)`