Lesson Vocabulary

• system of linear equations
• solution of a system of linear equations
• consistent
• independent
• dependent
• inconsistent

Problem 1 Solving a System of Equations by Graphing

What is the solution of the system? Use a graph.

y = x + 2 y = 3 x − 2 table with 2 rows and 3 columns , row1 column 1 , y , column 2 equals , column 3 x plus 2 , row2 column 1 , y , column 2 equals , column 3 3 x minus 2 , end table

Graph both equations in the same coordinate plane.

y = x + 2 The slope is  1 . The  y -intercept is  2 . y = 3 x − 2 The slope is  3 . The  y -intercept is − 2 . table with 2 rows and 4 columns , row1 column 1 , y , column 2 equals , column 3 x plus 2 , column 4 cap theslopeis . 1 . , cap the , y . minusinterceptis . 2 . , row2 column 1 , y , column 2 equals , column 3 3 x minus 2 , column 4 cap theslopeis . 3 . , cap the , y . minusinterceptis . minus 2 . , end table

Find the point of intersection. The lines appear to intersect at (2, 4). Check to see if (2, 4) makes both equations true.

Image Long Description

The solution of the system is (2, 4).