Question

How do you solve this system of equations `7x + 8y = - 10; - x + y = - 20`?

Answer 1

See a solution process below:

Explanation:

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

`-x + y = -20`

`color(red)(x) - x + y = color(red)(x) - 20`

`0 + y = x - 20`

`y = x - 20`

Step 2) Substitute `(x - 20)` for `y` in the first equation and solve for `x`:

`7x + 8y = -10` becomes:

`7x + 8(x - 20) = -10`

`7x + (8 xx x) - (8 xx 20) = -10`

`7x + 8x - 160 = -10`

`(7 + 8)x - 160 = -10`

`15x - 160 = -10`

`15x - 160 + color(red)(160) = -10 + color(red)(160)`

`15x - 0 = 150`

`15x = 150`

`(15x)/color(red)(15) = 150/color(red)(15)`

`(color(red)(cancel(color(black)(15)))x)/cancel(color(red)(15)) = 10`

`x = 10`

Step 2) Substitute `10` for `x` in the solution to the second equation at the end of Step 1 and calculate `y`:

`y = x - 20` becomes:

`y = 10 - 20`

`y = -10`

The Solution Is:* `x = 10` and `y = -10` or `(10, -10)`