solving systems of linear inequalities worksheet pkt with answers
TRANSCRIPT
Name____________________ Date_________ Class_________________
Page 1 of 9 ©Steve Weiss 2013
Solving Systems of Linear Inequalities Common Core:
Graph the solution to a linear inequality in two variables as a half-plane (excluding the boundary in case of a strict inequality), and graph the solution set to a system of linear
inequalities in two variables as the intersection of the corresponding half-planes Read through the following problem. If you see any missing information please fill it in.
problem scenario: You collect two types of Legos, the star wars model, and the ninja model. You would like to buy at least 25 sets for your collection. The star wars model costs $60.00. The ninja model costs $40.00. Furthermore, you can spend at most, $1200.00. Write a system of linear inequalities that models the various numbers of Lego models of each type that you could purchase. Step 1: Define variables
Let s = # of star wars models purchased
Let n = Step 2: Write a system of linear inequalities: (at least implies ! and at most implies ! ).
s + n ! 25 ----------> inequality 1 60s + 40n ! 1200 ----------> inequality 2 Step 3: Graph inequality 1 as follows:
First change inequality 1 to an equation as follows:
s + n = 25 ------------ > equation 1 Find the s-intercept for equation 1 by substituting 0 in for n and solving for s.
Find the n-intercept for equation 1 by substituting 0 in for s and solving for n
s + n = 25 s + n = 25 s + 0 = 25 0 + n = 25 s = 25 ------> s intercept n = 25 -----> n intercept for
for equation 1 for equation 2
Name____________________ Date_________ Class_________________
Page 2 of 9 ©Steve Weiss 2013
Step 4: You will need to complete this step
Graph the equation from step 3 by plotting the intercepts on the coordinate plane below. Recall that inequality 1 in step 2 states that: s + n ! 25. The ! in this situation means that you shade above the line. So you will need to do this as well.
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Name____________________ Date_________ Class_________________
Page 3 of 9 ©Steve Weiss 2013
Step 5: Repeat steps #3 - 4 for inequality 2 as follows: Write inequality 2 from step 2 in the box below:
Change inequality 2 to an equation. Call this equation 2: Find the s-intercept and n-intercept for equation 2. Show your work in the box below: (refer to step 3 for guidance).
Name____________________ Date_________ Class_________________
Page 4 of 9 ©Steve Weiss 2013
Step 6: You will need to complete this step
Graph the equation from step 5 by plotting the intercepts on the coordinate plane below. Please recall that the inequality in step 2 states that: 60s + 40n ! 1200 . The ! in this situation means that you shade below the line. You will need to do this as well.
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Name____________________ Date_________ Class_________________
Page 5 of 9 ©Steve Weiss 2013
Step 7: You will need to complete this step
Copy your graph and your shading from steps 4 and your graph and shading from step 6 onto the coordinate plane below.
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Page 6 of 9 ©Steve Weiss 2013
Step 8: You will need to complete this step
Look at you’re graph in step 7 and identify where the shadings overlap. You will need to make one final graph just as in step 7, but only include the overlapped shadings
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Name____________________ Date_________ Class_________________
Page 7 of 9 ©Steve Weiss 2013
Questions pertaining to problem scenario 1 Please refer to your final graph in step 8 to answer the following questions Recall the original inequalities from step 2 written below:
s + n ! 25 ----------> inequality 1 60s + 40n ! 1200 ----------> inequality 2
a. Pick a point in the shaded region of your graph in step 8 and verify that it is a
solution of both linear inequalities above:
b. Pick another point in the shaded region of your graph in step 8 and verify that it is a is solution of both linear inequalities above:
c. Now pick a third point that is in the shaded region and verify that it is a solution
to both inequalities above. d. How many solutions does this problem have? Please explain your answer in
complete sentences.
Name____________________ Date_________ Class_________________
Page 8 of 9 ©Steve Weiss 2013
Exercises: Graph the following systems of linear inequalities. Check one of your solutions. 1) 2x + 3y < 12 2) 4x – 5y ! 20
-5x + 7y ! 35 - 3x – 6y < 18 for problem #1 for problem #2
Check on solution below Check one solution below
Name____________________ Date_________ Class_________________
Page 9 of 9 ©Steve Weiss 2013
3) y < -2x !+!4 4) y > 3x – 3
y > 12x !!!2 y ! ! 2
3x + 1
for problem #3 for problem #4
Check one solution below Check one solution below
Key: Solving Systems of Linear Inequalities ©Steve Weiss 2013
Key
Systems of Linear Inequalities
Problem Scenario Step 1: n = # of ninja models Step 4 : s intercept = 25, n intercept = 25; solid line shaded above (check student
graph for accuracy) Step 5: box 1: 60s + 40n
!
" 1200 box 2: 60s + 40n = 1200 box 3: s intercept = 20, n intercept = 30 Step 6: s intercept = 20, n intercept = 30; solid line shaded below (check student
graph for accuracy) Step 8:
Key: Solving Systems of Linear Inequalities ©Steve Weiss 2013
Question pertaining to problem scenario 1: a – c: check students’ work d: Any point in the shaded region from step 8 is a possible solution. Exercises: 1.
Key: Solving Systems of Linear Inequalities ©Steve Weiss 2013
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Key: Solving Systems of Linear Inequalities ©Steve Weiss 2013
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Key: Solving Systems of Linear Inequalities ©Steve Weiss 2013
4.