Question

How do you solve the system of equations `4x + 3y = - 13` and `2x - 2y = 18`?

Answer 1

See a solution process below:

Explanation:

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

`2x - 2y = 18`

`2x - 2y + color(red)(2y) = 18 + color(red)(2y)`

`2x - 0 = 18 + 2y`

`2x = 18 + 2y`

`(2x)/color(red)(2) = (18 + 2y)/color(red)(2)`

`(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = 18/color(red)(2) + (2y)/color(red)(2)`

`x = 9 + y`

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

`4x + 3y = -13` becomes:

`4(9 + y) + 3y = -13`

`(4 xx 9) + (4 xx y) + 3y = -13`

`36 + 4y + 3y = -13`

`36 + (4 + 3)y = -13`

`36 + 7y = -13`

`-color(red)(36) + 36 + 7y = -color(red)(36) - 13`

`0 + 7y = -49`

`7y = -49`

`(7y)/color(red)(7) = -49/color(red)(7)`

`(color(red)(cancel(color(black)(7)))y)/cancel(color(red)(7)) = -7`

`y = -7`

Step 3) Substitute `-7` for `y` in the solution to the second equation at the end of Step 1 and calculate `x`:

`x = 9 + y` becomes:

`x = 9 - 7`

`x = 2`

The solution is: `x = 2` and `y = -7` or `(2, -7)`