Question

What values of a and b would make the equation shown have infinitely many solutions? 3x=ax+b

Answer 1

Infinitely many solutions means that you have the same thing on both sides of the equation no matter what value of x you plug in, right?

We just need both sides to be 3x then, correct?

If a were equal to 3 and b were equal to 0, we'd have

3x = (3)x + 0

Which is essentially 3x = 3x

So that means a = 3 and b = 0 must work!
Let's say x = 5

3(5) = 3(5) + 0

15 = 15 + 0

15 = 15

That means that a = 3 and b = 0 is your final answer :)