Question

How do you solve `2x + y = 3`, `x - 3y = 5`?

Answer 1

See a solution process below:

Explanation:

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

`2x + y = 3`

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

`0 + y = 3 - 2x`

`y = 3 - 2x`

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

`x - 3y = 5` becomes:

`x - 3(3 - 2x) = 5`

`x - (3 * 3) + (3 * 2x) = 5`

`x - 9 + 6x = 5`

`1x + 6x - 9 = 5`

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

`7x - 9 = 5`

`7x - 9 + color(red)(9) = 5 + color(red)(9)`

`7x - 0 = 14`

`7x = 14`

`(7x)/color(red)(7) = 14/color(red)(7)`

`(color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7)) = 2`

`x = 2`

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

`y = 3 - 2x` becomes:

`y = 3 - (2 * 2)`

`y = 3 - 4`

`y = -1`

The Solution Is:

`x = 2` and `y = -1`

Or

`(2, -1)`