Question

How do you solve `2x-4y=4` and `x + 4y = 14`?

Answer 1

See a solution process below:

Explanation:

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

`x + 4y = 14`

`x + 4y - color(red)(4y) = 14 - color(red)(4y)`

`x + 0 = 14 - 4y`

`x = 14 - 4y`

Step 2) Substitute `(14 - 4y)` for `x` in the first equation and solve for `y`:

`2x - 4y = 4` becomes:

`2(14 - 4y) - 4y = 4`

`(2 * 14) - (2 * 4y) - 4y = 4`

`28 - 8y - 4y = 4`

`28 + (-8 - 4)y = 4`

`28 + (-12)y = 4`

`28 - 12y = 4`

`-color(red)(28) + 28 - 12y = -color(red)(28) + 4`

`0 - 12y = -24`

`-12y = -24`

`(-12y)/color(red)(-12) = (-24)/color(red)(-12)`

`(color(red)(cancel(color(black)(-12)))y)/cancel(color(red)(-12)) = 2`

`y = 2`

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

`x = 14 - 4y` becomes:

`x = 14 - (4 * 2)`

`x = 14 - 8`

`x = 6`

The Solution is: `x = 6` and `y = 2` or `(6, 2)`

Answer 2

See below

`x=6" "y=2`

Explanation:

To solve `2x−4y=4` and `x+4y=14` , Add the two together

`" "2x−4y=4`
`" "x+4y=14`

`3x=18" "x=6`

substitute this into one of the equations

`x+4y=14" "6+4y=14`

`4y=8" "y=2`