Question

How do you solve 9x + 2y = 5 and y - 2x + 3 = 0?

Answer 1

`x = 11/13` and `y = -17/13`

Explanation:

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

`y - 2x + 3 + color(red)(2x - 3) = 0 + color(red)(2x - 3)`

`y - 2x + color(red)(2x) + 3 - color(red)(3) = 0 + 2x - 3`

`y - 0 + 0 = 2x - 3`

`y = 2x - 3`

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

`9x + 2(color(red)(2x - 3)) = 5`

`9x + 4x - 6 = 5`

`(9 + 4)x - 6 = 5`

`13x - 6 = 5`

`13x - 6 + color(red)(6) = 5 + color(red)(6)`

`13x - 0 = 11`

`13x = 11`

`(13x)/color(red)(13) = 11/color(red)(13)`

`(color(red)(cancel(color(black)(13)))x)/color(red)(cancel(color(black)(13))) = 11/13`

`x = 11/13`

Step 3) Substitute `11/13` for `x` in the solution to the second equation in Step 1) and calculate `y`:

`y = 2(color(red)(11/13)) - 3`

`y = 22/13 - 3`

`y = 22/13 - (3 * 13/13)`

`y = 22/13 - 39/13`

`y = -17/13`