Question

How do you solve `7x+2y=-31` and `-5x+y=27` using substitution?

Answer 1

See the entire solution process below:

Explanation:

Step 1) Solve the second equation for `y`:

`-5x + y = 27`

`color(red)(5x) - 5x + y = color(red)(5x) + 27`

`0 + y = 5x + 27`

`y = 5x + 27`

Step 2) Substitute `5x + 27` for `y` in the first equation and solve for `x`:

`7x + 2y = -31` becomes:

`7x + 2(5x + 27) = -31`

`7x + (2 * 5x) + (2 * 27) = -31`

`7x + 10x + 54 = -31`

`17x + 54 = -31`

`17x + 54 - color(red)(54) = -31 - color(red)(54)`

`17x + 0 = -85`

`17x = -85`

`(17x)/color(red)(17) = -85/color(red)(17)`

`(color(red)(cancel(color(black)(17)))x)/cancel(color(red)(17)) = -5`

`x = -5`

Step 3) Substitute `-5` for `x` in the solution to the second equation at the end of Step 1 and calculate `y`:

`y = 5x + 27` becomes:

`y = (5 * -5) + 27`

`y = -25 + 27`

`y = 2`

The solution is: `x = -5` and `y = 2` or `(-5, 2)`