Question

Is (-5, -1) a solution to this system of equations `3y = -2x - 13` and `-4x = -8y+12`?

Answer 1

Because `(-5, -1)` is a solution for both equations it is also a solution for the system of those two equations.

Explanation:

First, substitute `color(red)(-5) and`color(blue)(-1)`for`color(red)(x) and `color(blue)(y)` in the first equation and see if both sides of the equation calculate to the same value:

`3color(blue)(y) = -2color(red)(x) - 13` becomes:

`3 xx color(blue)(-1) = (-2 xx color(red)(-5)) - 13`

`-3 = 10 - 13`

`-3 = -3`

The first, equation has `(-5, -1)` as a solution. Now, substitute `color(red)(-5) and`color(blue)(-1)`for`color(red)(x) and `color(blue)(y)` in the second equation and see if both sides of the equation calculate to the same value:

`-4color(red)(x) = -8color(blue)(y) + 12` becomes:

`-4 xx color(red)(-5) = (-8 xx color(blue)(-1)) + 12`

`20 = 8 + 12`

`20 = 20`