Question

The graph shows the system 3x + 6y = 18 and x + 2y = 6. What is the solution for the system?


A. one solution
B. no solution
C. infinitely many solutions
D. cannot be determined
I say one solution

Answer 1

infinitely many solutions

Answer 2

Try (2, 2). That's a solution. But (4, 1) also works. Why?

3x + 6y = 18
x + 2y = 6
Multiply both sides of second equation by 3.
3x + 6y = 18

They're the same exact thing! If something works in the first one, it'll work for the second, so there are infinitely many solutions.