Solve Systems of Equations by Graphing: example 5.3

Solve the system by graphing: ${\begin{matrix} y = 2 x + 1 \\ y = 4 x - 1 \end{matrix} .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve each system by graphing: ${\begin{matrix} y = 2 x + 2 \\ y = − x - 4 \end{matrix} .$

How did it go?

Find the slope and y-intercept of the first equation.
Find the slope and y-intercept of the first equation.
Graph the two lines.
Determine the point of intersection.	The lines intersect at (1, 3).

Check the solution in both equations.	$\begin{matrix} \begin{matrix} y & = & 2 x + 1 \\ 3 & \overset{?}{=} & 2 \cdot 1 + 1 \\ 3 & = & 3 ✓ \end{matrix} & \begin{matrix} y & = & 4 x - 1 \\ 3 & \overset{?}{=} & 4 \cdot 1 - 1 \\ 3 & = & 3 ✓ \end{matrix} \end{matrix}$
	The solution is (1, 3).

Find the slope and y-intercept of the first equation.
Find the slope and y-intercept of the first equation.
Graph the two lines.
Determine the point of intersection.	The lines intersect at (1, 3).

Check the solution in both equations.	$\begin{matrix} \begin{matrix} y & = & 2 x + 1 \\ 3 & \overset{?}{=} & 2 \cdot 1 + 1 \\ 3 & = & 3 ✓ \end{matrix} & \begin{matrix} y & = & 4 x - 1 \\ 3 & \overset{?}{=} & 4 \cdot 1 - 1 \\ 3 & = & 3 ✓ \end{matrix} \end{matrix}$
	The solution is (1, 3).