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

1 Answer
KillerBunny
May 15, 2018

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=0x=0, we have 4y=24 \implies y=64y=24⇒y=6. So, (0,6)(0,6) is a solution
  • if we fix y=10y=10, we have 3x + 40 = 243x+40=24 and thus x=-16/3x=−163. So, (-16/3, 10)(−163,10) 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=243x+4y=24 is the equation of a line, which indeed has infinitely many points. So, once you choose any xx you want, you will have

y = \frac{24-3x}{4}y=24−3x4

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

x = \frac{24-4y}{3}x=24−4y3

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