Question

How many possible numbers of solutions are there to the system of equations?

Answer 1

Explanation:

Assuming a system of linear equations:

If the equations have the same slope, there are no possible solutions. Lines with the same slope run parallel and never intersect. Without an intersection, there is no solution. The solution is the point of intersection of graphs.

If the equations are equivalent, there are an infinite number of solutions. Equations can be equivalent in many ways. If one equation is rearranged to isolate one of its variables, the new equations looks different but it is equivalent. (Most commonly, two equivalent equations are in different forms, like standard, slope-intercept or point-intercept). If an equation has all of its terms multiplied or divided by the same number, the new equation is equivalent.

In any other case, there is only one solution.