Question

How do you solve the following system?: `x -9y =-2 , -2x +5y = -9`

Answer 1

See the entire solution process below:

Explanation:

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

`x - 9y = -2`

`x - 9y + color(red)(9y) = -2 + color(red)(9y)`

`x - 0 = -2 + 9y`

`x = -2 + 9y`

Step 2) Substitute `-2 + 9y` for `x` in the second equation and solve for `y`:

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

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

`(-2 * -2) + (-2 * 9y) + 5y = -9`

`4 - 18y + 5y = -9`

`4 + (-18 + 5)y = -9`

`4 + (-13)y = -9`

`4 - 13y = -9`

`-color(red)(4) + 4 - 13y = -color(red)(4) - 9`

`0 - 13y = -13`

`-13y = -13`

`(-13y)/color(red)(-13) = (-13)/color(red)(-13)`

`(color(red)(cancel(color(black)(-13)))y)/cancel(color(red)(-13)) = 1`

`y = 1`

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

`x = -2 + 9y` becomes:

`x = -2 + (9 * 1)`

`x = -2 + 9`

`x = 7`

The solution is: `x = 7` and `y = 1` or `(7, 1)`