Question

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

Answer 1

The second equation is just double the first, so the solution of this system is all pairs (x,y) satisfying x+y=3.

Answer 2

These equation do not have a solution because one is twice the other therefore independent. For solution to be obtainable equation must be independent.

Answer 3

Actually it has infinitely many solutions. For example, (0,3) or (1,2) or (100,-97) ... See my previous post for the way to express the complete solution set.

Answer 4

I know there lines coincide or are parallel, but when taking a difference you get zero indicating no single intersection which is required for solution

Answer 5

The lines coincide. Every point on the line, either line, is a solution. This should not be confused with linear independence or "no solution."

Answer 6

Actually the are parallel, its only when you multiply the first equation by 2 do they coincide.
y=mx+b
(2y)=m(2x)+2b
do these to equation coincide if you graph them as is?

Answer 7

KenLJW please excuse me, and with all due respect, I believe you are mistaken.

Answer 8

2(y=mx+b)
y=mx+2b
y=mx which is the solution of infinite points
notice these lines are parallel

Answer 9

To make it more clearly
y=mx+b
y=mx+2b
2(y=mx+b) -(y=mx+2b)=(y=mx)