Question

How do you solve the system of equations `6x + 3y = - 48` and `- 18x - 9y = 144`?

Answer 1

See a solution process below:

Explanation:

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

`6x + 3y = -48`

`-color(red)(6x) + 6x + 3y = -color(red)(6x) - 48`

`0 + 3y = -6x - 48`

`3y = -6x - 48`

`(3y)/color(red)(3) = (-6x - 48)/color(red)(3)`

`(color(red)(cancel(color(black)(3)))y)/cancel(color(red)(3)) = (-6x)/color(red)(3) - (48)/color(red)(3)`

`y = -2x - 16`

Step 2) Substitute `(-2x - 16)` for `y` in the second equation and solve for `x`:

`-18x - 9y = 144` becomes:

`-18x - 9(-2x - 16) = 144`

`-18x + (-9 xx -2x) + (-9 xx -16) = 144`

`-18x + 18x + 144 = 144`

`0 + 144 = 144`

`144 = 144`

Because these two values are equal we know these two equations are just different equations for the same lines. Therefore, for every point which is a solution to the first equation it is also a solution to the second equation.