Question

If you have a system of two equations with two unknowns and the two lines intersect on the graph, the systems have how many solutions?

Answer 1

In the figure above, there are three graphs labeled A, B, and C.
These three graphs show the three situations you can have with a system of two linear equations in two variables.

In graph A, the two lines are parallel. The lines never intersect. There is no point that is on both lines. Therefore, there is no solution to the system of equations.

In graph B, the two equations have the same line as a graph. All points of both equations are on the same line. Every point on the line is a solution to the system of equations, and there is an infinite number of solutions.

In graph C, the two lines intersect at exactly one point. That point is in both lines and is a solution to both equations. The point of intersection of the lines is the solution of the system of equations. There is exactly one solution.

Answer 2

Okay, thank you very much :)