Question

How do you solve the following system: `-6x + y = -8, 2x+3y =4`?

Answer 1

See a solution process below:

Explanation:

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

`-6x + y = -8`

`-6x + color(red)(6x) + y = -8 + color(red)(6x)`

`0 + y = -8 + 6x`

`y = -8 + 6x`

Step 2) Substitute `(-8 + 6x)` for `y` in the second equation and solve for `x`

`2x + 3y = 4` becomes:

`2x + 3(-8 + 6x) = 4`

`2x + (3 xx -8) + (3 xx 6x) = 4`

`2x - 24 + 18x = 4`

`2x + 18x - 24 = 4`

`(2 + 18)x - 24 = 4`

`20x - 24 = 4`

`20x - 24 + color(red)(24) = 4 + color(red)(24)`

`20x - 0 = 28`

`20x = 28`

`(20x)/color(red)(20) = 28/color(red)(20)`

`(color(red)(cancel(color(black)(20)))x)/cancel(color(red)(20)) = 7/5`

`x = 7/5`

Step 3) Substitute `7/5` for `x` in the solution to the first equation at the end of Step 1 and calculate `y`:

`y = -8 + 6x` becomes:

`y = -8 + (6 xx 7/5)`

`y = (5/5 xx -8) + 42/5`

`y = -40/5 + 42/5`

`y = 2/5`

The Solution Is:

`x = 7/5` and `y = 2/5`

Or

`(7/5, 2/5)`