Graphing System of Equations Worksheet

							Name:____________________________________ Date:__________________
Glencoe Algebra I – 7.1 Graphing Systems of Equations
Christine Hall

Objective
       Determine whether a system o linear equation has 0, 1, of infinitely many solutions.
       Solve systems of equations by graphing.

Material
       Mobile Lab Computer Support
       One computer with projection device to demonstrate
       Rulers, pencils, worksheet and graphing paper for each student

Classroom Setup
Each student will be working in groups of two.

Launch
See Screen for Five-Minute Check

Explore
1. Mini-lesson using first page of worksheet and table on page 369.
2. Activity using worksheet and gizmo
http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=120
or, if that does not connect, go to
http://www.explorelearning.com and select the “Solving Linear Systems by Graphing gizmo

Summary
See closing questions on worksheet. Students will answer them independently after a full group
summary of the activity and its key components.
Name:_____________________________________________ Date___________

Glencoe Algebra I – 7.1 Graphing Systems of Equations

Objective
       Determine whether a system of linear equation has 0, 1, of infinitely many solutions.
       Solve systems of equations by graphing.

Where to go
http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=120
or, if this does not connect, go to www.explorelearning.com and select Solving Linear Systems by
graphing

Lesson on Systems of Equations:

A - review. A linear system is formed by two or more linear equations. In chapter 5 you studied two
very specific types of systems of equations.

What are the names of the systems you already know? _____________________________ and

_______________________

How are their slopes related?



B - new. We can expand our view of systems by analyzing various lines with different slopes. Turn
to page 369. The table at the bottom of the page summarizes three categories of systems of linear
equations. On a graph, the solution to a linear system is represented by the intersection of the lines
corresponding to each equation. Compare the intersections of the three systems shown in the table.
Copy the table for your reference.




   1. Set the equation to standard form by clicking on the STANDARD tab. Using the sliders, set
      the first equation to 2x − y = −4 and the second equation to −x + 2y = −1.
1. Will all points on the line corresponding to 2x − y = −4 be valid solutions to this
   linear system? Why or why not? Rewiew the meaning of “solution” above.




2. The x–intercept of 2x − y = −4 is (−2, 0). Find this point on the graph. Is the point
   (−2, 0) also a solution to the equation −x + 2y = −1? Verify your answer
   algebraically and on the graph.




3. Find a point on the graph whose coordinates are solutions to both equations in the
   system.




4. Turn on Check solution at the point and drag the moveable point to this location to
   verify your answer.
       5. Move the point to other locations on the graph. Do you expect to find other ordered
          pairs that are solutions to the system of equations? Why or why not?



2. Determine algebraically if (1, −2) is a solution to the following system of equations: 2x − y =
   4 and x − y = 2. Graph this system using the Gizmo to check your answer.
3. Set the equation to slope–intercept form by clicking on the SLOPE–INTERCEPT tab.




Using the sliders, set the first equation to y = 2x + 5 and the second equation to y = 2x + 7.

       1. What do you notice about these two lines?



       2. Will any of the points on the line corresponding to y = 2x + 5 be valid solutions to
          this linear system? Why or why not?



       3. Is there a valid solution to this linear system? Explain your answer.



4. Set the equation to standard form by clicking on the STANDARD tab. Using the sliders, set
   the first equation to 2x − y = 3 and the second equation to −4x + 2y = −6.
       1. What do you notice about these two lines?



       2. Will all points on the line corresponding to 2x − y = 3 be valid solutions to this linear
          system? Why or why not?
C. – summary and independent time

1. Re-read the packet from the beginning. Go over your answers slowly and think about them. Does
what you wrote make sense? Would a friend who was absent today be able to learn from your
work?


2. Highlight any areas questions or answers that you still don’t feel you understand.


3. Meeting our objectives.
       a. What type of system has no, or 0, solutions? Explain with words, a system of equations,
and a graph. (three components to the answer)




        b. What type of system has 1 solution? Explain with words, a system of equations, and a
graph. (three components to the answer)




       c. What type of system has infinitely many solutions? Explain with words, a system of
equations, and a graph. (three components to the answer)