Question

How do you solve `2x+3y=21` and `-3x-6y=-24`?

Answer 1

See the entire solution process below:

Explanation:

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

`-3x - 6y = -24`

`-3x - 6y + color(red)(6y) = -24 + color(red)(6y)`

`-3x - 0 = -24 + 6y`

`-3x = -24 + 6y`

`(-3x)/color(red)(-3) = (-24 + 6y)/color(red)(-3)`

`(color(red)(cancel(color(black)(-3)))x)/cancel(color(red)(-3)) = (-24)/color(red)(-3) + (6y)/color(red)(-3)`

`x = 8 - 2y`

Step 2) Substitute `8 - 2y` for `x` in the first equation and solve for `y`:

`2x + 3y = 21` becomes:

`2(8 - 2y) + 3y = 21`

`(2 xx 8) - (2 xx 2y) + 3y = 21`

`16 - 4y + 3y = 21`

`16 + (-4 + 3)y = 21`

`16 - y = 21`

`16 - y - color(red)(16) = 21 - color(red)(16)`

`16 - color(red)(16) - y = 5`

`0 - y = 5`

`-y = 5`

`-1 xx -y = -1 xx 5`

`y = -5`

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

`x = 8 - 2y` becomes:

`x = 8 - (2 xx -5)`

`x = 8 - (-10)`

`x = 8 + 10`

`x = 18`

The solution is: `x = 18` and `y = -5` or `(18, -5)`