college prep unit 4: systems of equations and inequalities
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College Prep Unit 4: Systems of Equations and Inequalities
Ms. Talhami 1
College Prep Unit 4: Systems of Equations
and Inequalities
Name_________________
College Prep Unit 4: Systems of Equations and Inequalities
Ms. Talhami 2
Helpful Vocabulary Word Definition/Explanation Examples/Helpful Tips
College Prep Unit 4: Systems of Equations and Inequalities
Ms. Talhami 3
Proportions Vocabulary Definition/Explanation Examples
Proportion
College Prep Unit 4: Systems of Equations and Inequalities
Ms. Talhami 4
College Prep Unit 4: Systems of Equations and Inequalities
Ms. Talhami 5
Direct Variation Vocabulary Definition/Explanation
Direct Variation
“varies directly”
Direct Variation Equation _________________________ Constant of Variation _________________________ Graphs of Direct Variations Tables of Direct Variations a) b) a) b)
Examples: 1) The cost of a taxi fare varies directly as the distance travelled. When the distance is 60 km, the cost is $35. Find the cost when the distance is 95 km. 2) The total cost of filling up your car with gas varies directly with the number of gallons of gasoline that you are purchasing. If a gallon of gas costs $2.25, how many gallons could you purchase for $18?
College Prep Unit 4: Systems of Equations and Inequalities
Ms. Talhami 6
Practice
College Prep Unit 4: Systems of Equations and Inequalities
Ms. Talhami 7
College Prep Unit 4: Systems of Equations and Inequalities
Ms. Talhami 8
Systems of Equations Vocabulary Definition/Explanation
System of Equations
Methods to Solving Linear Systems
Graphing Elimination Substitution
Solve Linear Systems by Graphing
College Prep Unit 4: Systems of Equations and Inequalities
Ms. Talhami 9
9) ! = − $
% & + 1
! = − )$ & + 1
College Prep Unit 4: Systems of Equations and Inequalities
Ms. Talhami 10
Extra Practice
Methods to Solving Linear Systems
Graphing Elimination Substitution
Solve Linear Systems by Elimination Examples: 1) 2& + 3! = 20 2) & + 2! = 11 −2& + ! = 4 −3& + ! = −5
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Equations in Standard FormID: 1
Name___________________________________
Period____Date________________©E F2B00143w oKMuItaaj 8SWoQfFtFwNa6rYeF 6LGLUCB.L i sAylCl8 srIi8gphBtwsR NrJeLsfepryvUegdF.m
Solving Systems by Graphing
Solve each system by graphing.
1)
2
x +
y = 1
x − 2
y = 8
x
y
−5 −4 −3 −2 −1 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
2)
3
x + 2
y = 4
x + 2
y = −4
x
y
−5 −4 −3 −2 −1 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
3)
4
x +
y = 1
x +
y = −2
x
y
−5 −4 −3 −2 −1 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
4)
x + 3
y = −9
5
x + 3
y = 3
x
y
−5 −4 −3 −2 −1 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
-1-
©O 025001n3p QK5uWtoat gSfoXfRtcwBaMrheK VLQLzCL.2 T HAOlkll or7iCgjhMtAsw 7rhegsWeJrovoeJdG.z Z iMfaCdxe6 3w9i3tchP EInnSfXi0nOi6tber iAclXgxeMbBriaH L1u.i Worksheet by Kuta Software LLC
Equations in Standard FormID: 1
Name___________________________________
Period____Date________________©E F2B00143w oKMuItaaj 8SWoQfFtFwNa6rYeF 6LGLUCB.L i sAylCl8 srIi8gphBtwsR NrJeLsfepryvUegdF.m
Solving Systems by Graphing
Solve each system by graphing.
1)
2
x +
y = 1
x − 2
y = 8
x
y
−5 −4 −3 −2 −1 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
2)
3
x + 2
y = 4
x + 2
y = −4
x
y
−5 −4 −3 −2 −1 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
3)
4
x +
y = 1
x +
y = −2
x
y
−5 −4 −3 −2 −1 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
4)
x + 3
y = −9
5
x + 3
y = 3
x
y
−5 −4 −3 −2 −1 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
-1-
College Prep Unit 4: Systems of Equations and Inequalities
Ms. Talhami 11
Practice
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Kuta Software - Infinite Algebra 1 Name___________________________________
Period____Date________________Solving Systems of Equations by Elimination
Solve each system by elimination.
1)
−4
x − 2
y = −12
4
x + 8
y = −24
2)
4
x + 8
y = 20
−4
x + 2
y = −30
3)
x −
y = 11
2
x +
y = 19
4)
−6
x + 5
y = 1
6
x + 4
y = −10
5)
−2
x − 9
y = −25
−4
x − 9
y = −23
6)
8
x +
y = −16
−3
x +
y = −5
7)
−6
x + 6
y = 6
−6
x + 3
y = −12
8)
7
x + 2
y = 24
8
x + 2
y = 30
9)
5
x +
y = 9
10
x − 7
y = −18
10)
−4
x + 9
y = 9
x − 3
y = −6
11)
−3
x + 7
y = −16
−9
x + 5
y = 16
12)
−7
x +
y = −19
−2
x + 3
y = −19
-1-
College Prep Unit 4: Systems of Equations and Inequalities
Ms. Talhami 12
College Prep Unit 4: Systems of Equations and Inequalities
Ms. Talhami 14
How to Graph Inequalities
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Kuta Software - Infinite Algebra 1 Name___________________________________
Period____Date________________Graphing Linear InequalitiesSketch the graph of each linear inequality.
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College Prep Unit 4: Systems of Equations and Inequalities
Ms. Talhami 15
College Prep Unit 4: Systems of Equations and Inequalities
Ms. Talhami 16
Solve Inequality Systems by Graphing
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Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________Systems of Inequalities
Sketch the solution to each system of inequalities.
1)
y
>
4
x
− 3
y
≥
−2
x
+ 3
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
2)
y
≥
−5
x
+ 3
y
> −2
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
3)
y
< 3
y
≤
−
x
+ 1
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
4)
y
≥
x
− 3
y
≥
−
x
− 1
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
-1-
College Prep Unit 4: Systems of Equations and Inequalities
Ms. Talhami 17
College Prep Unit 4: Systems of Equations and Inequalities
Ms. Talhami 18
More Practice
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Kuta Software - Infinite Algebra 1 Name___________________________________
Period____Date________________Solving Systems of InequalitiesSketch the solution to each system of inequalities.
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College Prep Unit 4: Systems of Equations and Inequalities
Ms. Talhami 19
College Prep Unit 4: Systems of Equations and Inequalities
Ms. Talhami 20
Extra Graph Paper
College Prep Unit 4: Systems of Equations and Inequalities
Ms. Talhami 21
Extra Graph Paper