+23254 An infinite number of solutions will occur if you have two equations that, when graphed, give the same line.
For instance, when trying to find the solution for these two equations: 2x + 3y = 6 and 4x + 6y = 12,
if you graph them, you will get the same line, drawn twice.
So, each solution of the first equation will also work in the second equation. Since the first equation contains an infinite number of points, and each point is a solution, you get an infinite number of solutions.
(This will also be true for other pictures, not just straight lines.)
+23254 An infinite number of solutions will occur if you have two equations that, when graphed, give the same line.
For instance, when trying to find the solution for these two equations: 2x + 3y = 6 and 4x + 6y = 12,
if you graph them, you will get the same line, drawn twice.
So, each solution of the first equation will also work in the second equation. Since the first equation contains an infinite number of points, and each point is a solution, you get an infinite number of solutions.
(This will also be true for other pictures, not just straight lines.)
