day 1 - brunswick school department · systems of equations in lesson 3.1 you learned how to...
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Copyright © McDougal Littell Inc.
Graphing Systems of EquationsIn Lesson 3.1 you learned how to estimate the solution of a linear system bygraphing. With a graphing calculator, you can get an answer that is very closeto, and sometimes exactly equal to, the actual solution.
� EXAMPLESolve the linear system using a graphing calculator.
5x + 3y = º154x º 2y = 45
� SOLUTION
Solve each equation for y.
Using a standard viewing window, graph the equations.
� The solution is about (4.77, º12.95).
� EXERCISESSolve the linear system using a graphing calculator.
1. y = x + 4 2. y = º2x + 13 3. 3x º y = 16y = 2x + 5 y = 6x º 5 º5x + 8y = 13
4. 5x + 2y = 6 5. 6x + 9y = º13 6. 2x + 8y = º53x º 3y = º5 ºx + 2y = 10 3x + 4y = 26
3
1 Enter the equations. It’s a good idea to use parentheses to enter fractions.
Use the Intersect feature to find the point where the graphs intersect.
4
2
5x + 3y = º15
3y = º5x º 15
y = º�35
�x º 5
4x º 2y = 45
º2y = º4x + 45
y = 2x º �425�
If the graphs do not intersect on thescreen, set a different viewing window.
(º1, 3) (2.25, 8.5)
3. �}11491}, }11199}�, or about
(7.42, 6.26)
4. �}187}, }3117}�, or about
(0.47, 1.82)
5. �º}12116}, }42
71}�, or about
(º5.52, 2.24)(26.25, º13.1875)
1 Planning the Activity
PURPOSETo solve a linear system using agraphing calculator.
MATERIALS• graphing calculator• Activity Support Master
(Chapter 3 Resource Book, p. 13)
PACING• Activity — 20 min
LINK TO LESSONStudents can use the techniquesof this activity to check Examples2 and 4 in Lesson 3.1.
2 Managing the Activity
CLASSROOM MANAGEMENTStudents can work on this activitywith a partner. In Step 1, encouragestudents to retain the fraction formsof the slope and y-intercept ratherthan rounding them to decimalform. This will ensure the mostaccurate solution.
ALTERNATIVE APPROACHThis activity can be done as a classdemonstration using a graphing calculator with an overhead display.
3 Closing the Activity
KEY DISCOVERYA graphing calculator can be used to find an accurate estimateof the solution to a linear system.
ACTIVITY ASSESSMENTWrite a procedure you can use tofind the solution to a linear systemusing a graphing calculator.Sample answer: Write the equationsin slope-intercept form. Graph themon the calculator. Adjust the viewingwindow to show the intersection.Use the intersect feature to find thecoordinates of the intersection.
Copyright © McDougal Littell Inc.
Graphing Systems of EquationsIn Lesson 3.1 you learned how to estimate the solution of a linear system bygraphing. With a graphing calculator, you can get an answer that is very closeto, and sometimes exactly equal to, the actual solution.
� EXAMPLESolve the linear system using a graphing calculator.
5x + 3y = º154x º 2y = 45
� SOLUTION
Solve each equation for y.
Using a standard viewing window, graph the equations.
� The solution is about (4.77, º12.95).
� EXERCISESSolve the linear system using a graphing calculator.
1. y = x + 4 2. y = º2x + 13 3. 3x º y = 16y = 2x + 5 y = 6x º 5 º5x + 8y = 13
4. 5x + 2y = 6 5. 6x + 9y = º13 6. 2x + 8y = º53x º 3y = º5 ºx + 2y = 10 3x + 4y = 26
3
1 Enter the equations. It’s a good idea to use parentheses to enter fractions.
Use the Intersect feature to find the point where the graphs intersect.
4
2
5x + 3y = º15
3y = º5x º 15
y = º�35
�x º 5
4x º 2y = 45
º2y = º4x + 45
y = 2x º �425�
If the graphs do not intersect on thescreen, set a different viewing window.
(º1, 3) (2.25, 8.5)
3. �}11491}, }11199}�, or about
(7.42, 6.26)
4. �}187}, }3117}�, or about
(0.47, 1.82)
5. �º}12116}, }42
71}�, or about
(º5.52, 2.24)(26.25, º13.1875)
1 Planning the Activity
PURPOSETo solve a linear system using agraphing calculator.
MATERIALS• graphing calculator• Activity Support Master
(Chapter 3 Resource Book, p. 13)
PACING• Activity — 20 min
LINK TO LESSONStudents can use the techniquesof this activity to check Examples2 and 4 in Lesson 3.1.
2 Managing the Activity
CLASSROOM MANAGEMENTStudents can work on this activitywith a partner. In Step 1, encouragestudents to retain the fraction formsof the slope and y-intercept ratherthan rounding them to decimalform. This will ensure the mostaccurate solution.
ALTERNATIVE APPROACHThis activity can be done as a classdemonstration using a graphing calculator with an overhead display.
3 Closing the Activity
KEY DISCOVERYA graphing calculator can be used to find an accurate estimateof the solution to a linear system.
ACTIVITY ASSESSMENTWrite a procedure you can use tofind the solution to a linear systemusing a graphing calculator.Sample answer: Write the equationsin slope-intercept form. Graph themon the calculator. Adjust the viewingwindow to show the intersection.Use the intersect feature to find thecoordinates of the intersection.
