The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 4.17: GRAPHING SYSTEMS OF LINEAR

EQUATIONS WHEN LINES INTERSECT

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Follow the steps below to find the solutions to systems of linear equations by graphing:

1. Write each equation in slope-intercept form (if it is not already in this form).


2. Graph both equations on the same coordinate plane.


3. Find the coordinates of the point of intersection. The point of intersection represents
   thesolutiontothesystem.


4. Check the coordinates algebraically by substituting each value into the original system
   of equations.

EXAMPLE

y= 3 x+ 4

y=x− 2

(−3,−5) is the point of inter-

section, which represents the

solution to the system.

DIRECTIONS: Solveeachsystemoflinearequations.

1. y= 3 x+ 6 2. y=x+ 6 3. y= 2 x− 1 4.y=−x+ 5
   y= 2 x+ 8 y=− 2 x− 9 y= 5 x− 4 y= 3 x+ 13


2. 2 y=− 3 x+ 4 6.y=− 2 x− 3 7. 5 y= 2 x+ 5 8.y+ 3 x= 4
   3 y=x− 5 y−x= 92 y=xy+x=− 2

CHALLENGE:Mike solved a system of linear equations by graphing. The

solutions were not integers. How might he have solved this system of

equations? Explain your reasoning.

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.