Question

Consider the two equations you underlined, which form a system with one solution. Graph them together on the following coordinate grid.

y = -2x + 3 and y = 3x + 1

What do you notice about these equations? What does it mean for a system to have one solution? Explain what it means graphically for a system to have one solution.

Answer 1

When graphed together, these two equations intersect at a single point. This is because a system of equations has one solution when the two lines represented by the equations intersect at a single point. Graphically, this means that the two lines are not parallel or coincident, but instead intersect at a specific point where the x and y values satisfy both equations simultaneously. This is the solution to the system of equations.