Question

*** Anyone who answers randomly for points WILL be reported ***



Problem:

Give an example a linear equation in one variable with infinitely many solutions,
Explain how you know it has infinitely many solutions.

Answer 1

One example is the equation 2x+3x = 5x because the left hand side combines to form the right hand side. This equation is said to be an identity, which is always true for any real number you can think of. For example, if x = 3, then,

2x+3x = 5x

2*3+3*3 = 5*3 ... replace every x with 3

6 + 9 = 15

15 = 15

We end up with a true equation. This will happen regardless of what x value we pick. Therefore, it has infinitely many solutions.