Question

How do you solve the following linear system: `3x + 2y = –5 , x-2y=13`?

Answer 1

See a solution process below:

Explanation:

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

`x - 2y = 13`

`x - 2y + color(red)(2y) = 13 + color(red)(2y)`

`x - 0 = 13 + 2y`

`x = 13 + 2y`

Step 2) Substitute `(13 + 2y)` for `x` in the first equation and solve for `y`:

`3x + 2y = -5` becomes:

`3(13 + 2y) + 2y = -5`

`(3 * 13) + (3 * 2y) + 2y = -5`

`39 + 6y + 2y = -5`

`39 + (6 + 2)y = -5`

`39 + 8y = -5`

`39 - color(red)(39) + 8y = -5 - color(red)(39)`

`0 + 8y = -44`

`8y = -44`

`(8y)/color(red)(8) = -44/color(red)(8)`

`(color(red)(cancel(color(black)(8)))y)/cancel(color(red)(8)) = -(4 xx 11)/color(red)(4 xx 2)`

`y = -11/2`

Step 3) Substitute `-11/2` for `y` in the solution to the second equation at the end of Step 1 and calculate `x`:

`x = 13 + 2y` becomes:

`x = 13 + (2 xx -11/2)`

`x = 13 + (-11)`

`x = 2`

The Solution Is:

`x = 2` and `y = -11/2`

Or

`(2, -11/2)`