Question

How do you solve the system of equations `x+ 4y = 4` and `x - 2y = - 8`?

Answer 1

See the entire solution process below:

Explanation:

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

`x + 4y = 4`

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

`x + 0 = 4 - 4y`

`x = 4 - 4y`

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

`x - 2y = -8` becomes:

`(4 - 4y) - 2y = -8`

`4 - 4y - 2y = -8`

`4 - 6y = -8`

`-color(red)(4) + 4 - 6y = -color(red)(4) - 8`

`0 - 6y = -12`

`-6y = -12`

`(-6y)/color(red)(-6) = (-12)/color(red)(-6)`

`(color(red)(cancel(color(black)(-6)))y)/cancel(color(red)(-6)) = 2`

`y = 2`

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

`x = 4 - 4y` becomes:

`x = 4 - (4 xx 2)`

`x = 4 - 8`

`x = -4`

The solution is: `x = -4` and `y = 2` or `(-4, 2)`