Lesson Vocabulary

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

Problem 1 Using a Graph or Table to Solve a System

What is the solution of the system? { − 3 x + 2 y = 8 x + 2 y = − 8 left brace . table with 2 rows and 1 column , row1 column 1 , negative 3 x plus 2 y equals 8 , row2 column 1 , x plus 2 y equals negative 8 , end table

Method 1 Graph the equations. The point of intersection appears to be ( − 4 , − 2 ) . open negative 4 comma negative 2 close .

Check by substituting the values into both equations.

− 3 x + 2 y = 8   x + 2 y = − 8   − 3 ( − 4 ) + 2 ( − 2 ) = 8 ✓ − 4 + 2 ( − 2 ) = − 8 ✓ table with 2 rows and 4 columns , row1 column 1 , negative 3 x plus 2 y equals 8 , column 2 , column 3 x plus 2 y equals negative 8 , column 4 , row2 column 1 , negative 3 open negative 4 close plus 2 open negative 2 close equals 8 , column 2 check mark , column 3 negative 4 plus 2 open negative 2 close equals negative 8 , column 4 check mark , end table

Both equations are true so ( − 4 , − 2 ) open negative 4 comma negative 2 close  is the solution of the system.