Question

How do you solve the system of equations `2x + 9y = - 5` and `- 2x - 8y = - 6`?

Answer 1

See the entire solution process below:

Explanation:

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

`-2x - 8y = -6`

`-2x - 8y + color(red)(8y) = -6 + color(red)(8y)`

`-2x - 0 = -6 + 8y`

`-2x = -6 + 8y`

`(-2x)/color(red)(-2) = (-6 + 8y)/color(red)(-2)`

`(color(red)(cancel(color(black)(-2)))x)/cancel(color(red)(-2)) = (-6)/color(red)(-2) + (8y)/color(red)(-2)`

`x = 3 - 4y`

Step 2) Substitute `3 - 4y` for `x` in the first equation and solve for `y`:

`2x + 9y = -5` becomes:

`2(3 - 4y) + 9y = -5`

`(2 xx 3) - (2 xx 4y) + 9y = -5`

`6 - 8y + 9y = -5`

`6 + y = -5`

`-color(red)(6) + 6 + y = -color(red)(6) - 5`

`0 + y = -11`

`y = -11`

Step 3) Substitute `-11` for `y` in the solution to the second equation at the end of Step 1 and calculate `x`:

`x = 3 - 4y` becomes:

`x = 3 - (4 xx -11)`

`x = 3 - (-44)`

`x = 3 + 44`

`x = 47`

The solution is: `x = 47` and `y = -11` or `(47, -11)`