Question

What is the ordered pairs that satisfy the equation `7x+4y=-6`?

Answer 1

There is an infinite collection of ordered pairs which satisfy the given equation; a few examples are given in the image below:

Explanation:

`7x+4y=-6`

`rArr 4y = -7x-6`

`rArr y = -7/4x-6/4`
`color(white)("XXXXXXXXX")-6/4 = -1 1/2` but for hand calculations its probably better to leave it with the same denominator as `-7/4x`

Picking any arbitrary value for `x` lets you calculate the corresponding value for `y` that satisfies the given equation.

Note that if you are looking for integer pairs `(x,y)`
if `x` is an integer multiple of `4` minus `2` (`x in 4n-2, AAninZZ`)
then `y` will also be an integer.