Question

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

Answer 1

See a solution process below:

Explanation:

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

`x - 2y = -5`

`x - 2y + color(red)(2y) = -5 + color(red)(2y)`

`x - 0 = -5 + 2y`

`x = -5 + 2y`

Step 2) Substitute `(-5 + 2y)` for `x` in the first equation and solve for `y`:

`2x - 9y = 5` becomes:

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

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

`-10 + 4y - 9y = 5`

`-10 + (4 - 9)y = 5`

`-10 + (-5)y = 5`

`-10 - 5y = 5`

`color(red)(10) - 10 - 5y = color(red)(10) + 5`

`0 - 5y = 15`

`-5y = 15`

`(-5y)/color(red)(-5) = 15/color(red)(-5)`

`(color(red)(cancel(color(black)(-5)))y)/cancel(color(red)(-5)) = -3`

`y = -3`

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

`x = -5 + 2y` becomes:

`x = -5 + (2 * -3)`

`x = -5 + (-6)`

`x = -11`

The solution is: `x = -11` and `y = -3` or `(-11, -3)`