An infinite solution has both sides equal. For example, 6x + 2y - 8 = 12x +4y - 16. If you simplify the equation using an infinite solutions formula or method, you'll get both sides equal, hence, it is an infinite solution.

A system of equations that has infinite solutions will always yield an identity when solved (such as 0=0). Graphically, a system of equations with infinite solutions is two lines or planes lying on each other. An example would be: x+y=1 and 2x+2y=2.

Conditions for Infinite Solution The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line.

Sometimes we use the symbol ∞, which means infinity, to represent infinite solutions.