Question

How do solve the following linear system?: `3x + 2y = 12, y = 4x + 4`?

Answer 1

See a solution process below:

Explanation:

Step 1) Because the second equation is already solved for `y` we can substitute `(4x + 4)` for `y` in the first equation and solve for `x`:

`3x + 2y = 12` becomes:

`3x + 2(4x + 4) = 12`

`3x + (2 xx 4x) + (2 xx 4) = 12`

`3x + 8x + 8 = 12`

`(3 + 8)x + 8 = 12`

`11x + 8 = 12`

`11x + 8 - color(red)(8) = 12 - color(red)(8)`

`11x + 0 = 4`

`11x = 4`

`(11x)/color(red)(11) = 4/color(red)(11)`

`(color(red)(cancel(color(black)(11)))x)/cancel(color(red)(11)) = 4/11`

`x = 4/11`

Step 2) Substitute `4/11` for `x` in the second equation and solve for `y`:

`y = 4x + 4` becomes:

`y = (4 xx 4/11) + 4`

`y = 16/11 + 4`

`y = 16/11 + (4 xx 11/11)`

`y = 16/11 + 44/11`

`y = (16 + 44)/11`

`y = 60/11`

The Solution Is:

`x = 4/11` and `y = 60/11`

Or

`(4/11, 60/11)`