Question

How do you solve the system of linear equations `x + 3y = 8` and `2x - y = 9`?

Answer 1

See a solution process below:

Explanation:

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

`x + 3y = 8`

`x + 3y - color(red)(3y) = 8 - color(red)(3y)`

`x + 0 = 8 - 3y`

`x = 8 - 3y`

Step 2) Substitute `8 - 3y` for `x` in the second equation and solve for `y`:

`2x - y = 9` becomes:

`2(8 - 3y) - y = 9`

`(2 * 8) - (2 * 3y) - y = 9`

`16 - 6y - y = 9`

`16 - 6y - 1y = 9`

`16 - 7y = 9`

`-color(red)(16) + 16 - 7y = -color(red)(16) + 9`

`0 - 7y = -7`

`-7y = -7`

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

`(color(red)(cancel(color(black)(-7)))y)/cancel(color(red)(-7)) = 1`

`y = 1`

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

`x = 8 - 3y` becomes:

`x = 8 - (3 * 1)`

`x = 8 - 3`

`x = 5`

The solution is: `x = 5` and `y = 1` or `(5, 1)`