Question

Solving Systems without Unique Solutions

I'm having a bit of trouble as the problem below is suppose to be one that is always true which means the numbers have to be equal and cannot be zero, correct?

So anyways the problem;

4x + y = 6
12x + 3y = 18

12 (4x + y = 6)
-4 (12x + 3y = 18)

48x + 12y = 72
-48x - 12y = -72
0 = 0

What set did I mess up on?

Answer 1

Nothing is wrong, just infinite solutions.

Answer 2

if you find a point (x, y) that satisfies one of the equations, the same point will satisfy the other equation

Answer 3

Thanks, I thought something was wrong because I could have sworn I watched a video that said the equation had to equal one number to another number for it be an infinite number of solutions.

Also another quick question, for an equation to have no solution would that mean the answer would have to be something like 0 = 3?

Answer 4

yup

Answer 5

yes... if you get a true statement, like 3 = 3 or 0 = 0, then infinite solutions. if you get a false statement like 3 = 0 or 0 = 1 then no solutions.