Solving Systems of Linear Equations Graphically

To match the solutions with their system, we'll substitute the first point into the first system. If the point is a solution to both equations, it's a solution ot the system. The equality is true for the second equation but not for the first one. A solution to a system of equations has to satisfy all equations. Therefore, $(8,4)$ cannot be a solution to the first system. Let's try the second point, $(4,6).$ Both equations are satisfied for $(4,6).$ Thus, it's a solution to the system. Continue with B and check with the first point. It's a solution! This means that the last point must be a solution to the last system of equations. Let's find out. We have now paired the three solutions with the three systems. $$\begin{array}{rl}\text{A:}& (4,6)\\ \text{B:}& (8,4)\\ \text{C:}& (1,\text{-}3)\end{array}$$