Question

How many possible solutions are there for these equations? x - 3y = -3, -2x + 6y = 12

Answer 1

x - 3y = -3 (put in y = mx + b form)
-3y = -x - 3 -- divide both sides by -3
y = 1/3x + 1

-2x + 6y = 12 (put in y = mx + b form)
6y = 2x + 12 -- divide both sides by 6
y = 1/3x + 2

okay...learn this

if the slopes (numbers in the m position) are the same, and the y intercept (numbers in the b position) are the same, then it is the same line with infinite solutions.

if the slopes are the same and the y intercepts different, then it is a parallel line with no solutions because the lines never intersect.

if the slopes are different and the y intercepts different, then it just has one solution

conclusion :
slopes are the same, y intercepts are different..making the lines parallel with no solutions