Solving Systems of Linear Equations Graphically

Let's solve the system of equations by graphing. Thus, we must identify each line's key features.

Now, we can graph the equations.

We can see that the graphs intersect at the point $(6,\text{-}2).$ This is the solution of the system of the equations.

The equation in part A is $$\frac{1}{3}x-4=\text{-}2x+10.$$ The system of equations from part B is $$\{\begin{array}{l}y=\frac{1}{3}x-4\\ y=\text{-}2x+10.\end{array}$$ The first function in the system corresponds to the left-hand side in the equation.

$$\begin{array}{rl}\text{Part A:}& x=6\\ \text{Part B:}& (6,\text{-}2)\end{array}$$ As discussed in part C, the left- and right-hand side of the equation in part A represented the functions in part B. Therefore, the $x$-value is the same in the two answers. $$\begin{array}{rl}\text{Part A:}& x=6\\ \text{Part B:}& (6,\text{-}2)\end{array}$$ However, in part B we got a value of $y$ as well. This is because the equations are separated in part B but not in part A.