5x - 3y = 10
10x + 6y= 20
Multiply the first equation by 2, and subtract the 2nd equation:
10x - 6y = 20
-
10x + 6y = 20
___________
0x + 0 y = 0
0 = 0
Since both variables were eliminated and the statement is true 0=0, there are infinitely many solutions.