Question

How do you solve and find the ordered pairs `1/2 x - 2y = 4 and 4y - x = -8`?

Answer 1

Using `x = 4y+8" "` if you choose values of `y` you can find the corresponding values of `x` and hence obtain the ordered pairs.

Explanation:

The first equation can be changed into a better form by removing the fraction:

`2xx1/2x-2xx2y =2xx4" "xx` each term by `2`

`x-4y = 8`

the second equation can be rewritten as `x-4y =8`

We therefore see that there is actually only one equation, and as it has two variables, there are many solutions.

Using `x = 4y+8" "` if you choose values of `y` you can find the corresponding values of `x` and hence obtain the ordered pairs.

`y=0, rarr x=8" "rarr (8,0)`
`y=1, rarr x=12" "rarr (12,1)`
`y=2, rarr x=16" "rarr (16,2)`
`y=-1, rarr x=4" "rarr (4,-1)`
`y=-2, rarr x=0" "rarr (0,-2)`

IN this way you can generate as many ordered pairs as you need.