Question

Hello! I need a demonstration of how to find out how many solutions are in the following system of equations:

x + y = 3
2x + 2y = 6

I am not sure if there is an infinite amount of solutions or if there is no solution.

Answer 1

Hint, if you multiply the entire first equation by 2...what do you get?

Answer 2

You get: 2x + 2y = 6

Answer 3

But does that mean no solutions or infinite solutions? @johnweldon1993

Answer 4

Right, you get the 2nd equation...and if they are the same line...they lay completely on top of each other

and since solutions are where they intersect...and they ALWAYS intersect...there are an infinite amount of solutions

Answer 5

I thought it would mean infinite because if they are the same equation, then when put into Slope Intercept Form and then finally graphed, they would be the same line.

Answer 6

Hehe, we almost said the same thing. Glad to know I am on the right track, though! Thanks for your help! :)

Answer 7

Lol great minds think alike :D and of course anytime :)

Answer 8

:D

Answer 9

Do you think you could help me with another question? It's about graphing a system of equations.

Answer 10

Of course ^_^