Question

How do you use substitutions to solve `5x - 2y = - 19` and `x - 3y = - 9`?

Answer 1

See the entire solution process below:#

Explanation:

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

`x - 3y = -9`

`x - 3y + color(red)(3y) = -9 + color(red)(3y)`

`x - 0 = -9 + 3y`

`x = -9 + 3y`

Step 2) Substitute `-9 + 3y` for `x` in the first equation and solve for `y`:

`5x - 2y = -19` becomes:

`5(-9 + 3y) - 2y = -19`

`(5 xx -9) + (5 xx 3y) - 2y = -19`

`-45 + 15y - 2y = -19`

`-45 + 13y = -19`

`color(red)(45) - 45 + 13y = color(red)(45) - 19`

`0 + 13y = 26`

`13y = 26`

`(13y)/color(red)(13) = 26/color(red)(13)`

`(color(red)(cancel(color(black)(13)))y)/cancel(color(red)(13)) = 2`

`y = 2`

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

`x = -9 + 3y` becomes:

`x = -9 + (3 xx 2)`

`x = -9 + 6`

`x = -3`

The solution is: `x = -3` and `y = 2` or `(-3, 2)`