Question

How many solutions will this system of equations have?

x - 2y = 24
3x - 6y = 72

A) No solution
B) Infinite solutions
C) One solution
D) Two solutions

Answer 1

you see that the second equation is the same as the first one?

Answer 2

yeah

Answer 3

The second is just a multiple of the first, the same lines. 3 times the first.

Answer 4

If you graphed them, the second is overlayed on top of the first. It is one line.
There are infinitely many points (x,y) on a line

Answer 5

so b?

Answer 6

right, infinite solutions.

Lines either have one solution where they intersect (x,y)
Zero solutions if they never intersect, are parallel
infinite solutions if they are the same line

Answer 7

got it, thank you.

Answer 8

welcome