Chapter 6.1, Problem 1P

Solve each system by graphing. Check your solution.

$y=-x+3$

$y=4x-2$

To determine

To find: The solution of the system of equations:

  $\begin{array}{l}y=-x+3\\ y=4x-2\end{array}$

Answer to Problem 1P

The graph of the system is

  

The solution of the system of equations is $(1,2)$ .

Explanation of Solution

Given information:

The system is

  $\begin{array}{l}y=-x+3\\ y=4x-2\end{array}$

The equation $y=-x+3$ has the slope $-1$ and y -intercept of $3$ . So plot a point at $3$ on the y -axis. Then go down 1 right 1 from the y -intercept to plot a second point. Now, draw a line passing through these two points as shown in the graph in red color.

The equation $y=4x-2$ has the slope $4$ and y -intercept of $-2$ . So plot a point at $-2$ on the y -axis. Then go up 4 right 1 from the y -intercept to plot a second point. Now, draw a line passing through these two points as shown in the graph in blue color.

  

Conclusion:

Observing the graph, the two lines are intersecting at $(1,2)$ . Therefore, the solution of the system is $(1,2)$ .

To verify, let us substitute the solution into both equations.

  $\begin{array}{l}(1):\\ y=-x+3\\ 2=-1+3\\ 2=2(\text{True})\\ (2):\\ y=4x-2\\ 2=4(1)-2\\ 2=4-2\\ 2=2(\text{True})\end{array}$

Hence, verified.