Question

How do you solve the following linear system: `x+y=4, -3x+y=-8`?

Answer 1

See a solution process below:

Explanation:

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

`x + y = 4`

`x + y - color(red)(y) = 4 - color(red)(y)`

`x + 0 = 4 - y`

`x = 4 - y`

Step 2) Substitute `(4 - y)` for `x` in the second equation and solve for `y`:

`-3x + y = -8` becomes:

`-3(4 - y) + y = -8`

`(-3 xx 4) + (3 xx y) + y = -8`

`-12 + 3y + y = -8`

`-12 + color(red)(12) + 3y + y = -8 + color(red)(12)`

`0 + 3y + y = 4`

`3y + y = 4`

`3y + 1y = 4`

`(3 + 1)y = 4`

`4y = 4`

`(4y)/color(red)(4) = 4/color(red)(4)`

`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 = 4 - y` becomes:

`x = 4 - 1`

`x = 3`

The Solution Is:

`x = 3` and `y = 1`

Or

`(3, 1)`