Question

How do you solve the system of equations `2x + y = 8` and `3x - y = 7`?

Answer 1

See a solution process below:

Explanation:

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

`2x + y = 8`

`2x - color(red)(2x) + y = 8 - color(red)(2x)`

`0 + y = 8 - 2x`

`y = 8 - 2x`

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

`3x - y = 7` becomes:

`3x - (8 - 2x) = 7`

`3x - 8 + 2x = 7`

`3x - 8 + color(red)(8) + 2x = 7 + color(red)(8)`

`3x - 0 + 2x = 15`

`3x + 2x = 15`

`(3 + 2)x = 15`

`5x = 15`

`(5x)/color(red)(5) = 15/color(red)(5)`

`x = 3`

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

`y = 8 - 2x` becomes:

`y = 8 - (2 xx 3)`

`y = 8 - 6`

`y = 2`

**The Solution Is:

`x = 3` and `y = 2`

Or

`(3, 2)`