Question

What is the ordered pairs that satisfy the equation `3x + 4y = 24`?

Answer 1

There are infinitely many pairs

Explanation:

From an intuitive point of view, you may check how, once you arbitrarily fix a variable, you can find the corresponding value for the other. Here are some examples:

• if we fix `x=0`, we have `4y=24 \implies y=6`. So, `(0,6)` is a solution
• if we fix `y=10`, we have `3x + 40 = 24` and thus `x=-16/3`. So, `(-16/3, 10)` is another solution

as you may see, you can go on with this method to find all the points that you want.

The underlying reason is that `3x+4y=24` is the equation of a line, which indeed has infinitely many points. So, once you choose any `x` you want, you will have

`y = \frac{24-3x}{4}`

On the other hand, once you choose any random `y`, you will have

`x = \frac{24-4y}{3}`