What is the ordered pairs that satisfy the equation #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=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}#

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