### Home > CCG > Chapter 2 > Lesson 2.1.3 > Problem2-31

2-31.

The set of equations at right is an example of a system of equations. Read the Math Notes box for this lesson on how to solve systems of equations. Then answer the questions below.

$\begin{array}{l} y=-x+1 \\ y=2x+7 \end{array}$

Remember to read the Math Notes box for this lesson!

1. Graph the system on graph paper. Then write its solution (the point of intersection) in $(x,y)$ form.

The point of intersection is $(-2,3)$.

2. Now solve the system using an algebraic method of your choice. Did your solution match your result from part (a)? If not, check your work carefully and look for any mistakes in your algebraic process or on your graph.

$\begin{array}{l} -x + 1 = 2x + 7 \\ +x \qquad \; \; + x \\ \qquad \; \; 1 = 3x + 7 \\ \quad \; \; \; -7 = -7 \\ \quad \; \; \; -6 = 3x \\ \quad \; \; \; -2 = x \end{array}$

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

The solution is $(-2,3)$.

Use the eTool to graph the system.
Click the link at right for the full version of the eTool: 2-31 HW eTool