Question

How do you know how many solutions are possible for a system of equations

Answer 1

Explanation:

If you mean linear systems. If lines have a different slope there will be one solution. If they have the same slope (parallel) and a different y intercept there are zero solutions. If they have same slope and y intercept than they are the same line and have an infinite number of solutions.

Answer 2

Explanation:

If the slopes are the same but the y-intercepts are different, the system has no solution.

If the slopes are different, the system has one solution.

If the slopes are the same and the y-intercepts are the same, the system has infinitely many solutions.