5x + 6y =2, 10x + 12y = 4 Solve by elimination method?

Multiply the first equation by -2, then add the first to the second, this will cancel out the y's, then you can solve for x:

-10x - 12y = -4
10x + 12y = 4
0x + 0y = 0

These two equations are identicle lines, so there are infinately many solutions.

5x + 6y = 2
10x + 12y = 4

5x + 6y = 2
2(5x + 6y) = 2(2)
10x + 12y = 4

...10x + 12y = 4
-- 10x + 12y = 4 (subtraction)
------------------------
0x + 0y = 0
(they are the same line)
(many solutions)

the equations are exactly the same
there isn't one exact answer to this system

10x + 12y = 4 ---> eq1 multiplied by 2
10x + 12y = 4

The system has infinite solutions.

you can multiply the first equation by -2 and then add the resulting equation to the second equation. i.e.:
-2(5x + 6y) = -2(2)
-10x -12y = -4. adding this to the second equation you get 0 = 0, which implies that these are exactly the same equation, and there are infinitely many solutions.