MATH Integrated Math I  - Unit 32: System of Equations: Graphing and Substitution
Solving Equations and Simplifying Algebraic Expressions (Review)

For the first five problems, solve each equation algebraically.

1) Solve for “x”:  32 = 8 – 4x

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2) Solve for “x”:  12x + 22 = 10x – 4

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3) Solve for “x”:  –4 + 2x = 10x

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4) Solve for “x”:  6(3x – 9) = –18

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5) Solve for “x”:  2x + 6 = –3x – 3

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For the next three problems, solve the equation. State the letter of the correct answer.

6) Solve for “x”.

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7) Solve for “x”.

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8) Solve for “a”.

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Solving Systems of Equations Using Graphs

9) When solving a system of equations using graphing, if the lines of the two equations are parallel (do not intersect), what is true about the system of equations?

10) When solving a system of equations using graphing, if the lines of the two equations intersect, what is true about the system of equations?

11) When solving a system of equations using graphing, if the lines of the two equations are the same line, what is true about the system of equations?

12) The lines of two equations are graphed below. Name the ordered pair that is the solution of the two equations.

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13) The lines of two equations are graphed below. Name the ordered pair that is the solution of the two equations.

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14) The lines of two equations are graphed below. Name the ordered pair that is the solution of the two equations.

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The lines of several equations are graphed below. Refer to these lines to solve the next four problems. Click to view the graph of the lines in a pop-up window.

15) Does the system of equations represented by line “q” and line “r” have “one” solution or “no” solution? If the system has a solution, state the ordered pair for the solution.

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16) Does the system of equations represented by line “m” and line “n” have “one” solution or “no” solution? If the system has a solution, state the ordered pair for the solution.

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17) Does the system of equations represented by line “n” and line “q” have “one” solution or “no” solution? If the system has a solution, state the ordered pair for the solution.

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18) Does the system of equations represented by line “p” and line “q” have “one” solution or “no” solution? If the system has a solution, state the ordered pair for the solution.

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For the next four problems, graph each system in a coordinate plane on graph paper, and then state the solution.  There is a link to graph paper in the content area of this unit.  

19) Solve the system of equations and state the answer as an ordered pair.

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20) Solve the system of equations and state the answer as an ordered pair.

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21) Solve the system of equations and state the answer as an ordered pair.

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22) Solve the system of equations and state the answer as an ordered pair.

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Solving Systems of Equations Using Substitution

23) Solve the system of equations by using substitution. State the answer as an ordered pair.

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24) State an equation that can be written in the previous problem after making the first substitution. (Hint: See Step 2 in the examples in the unit link to "Solving Systems by Substitution".) 

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25) Solve the system of equations by using substitution. State the answer as an ordered pair.

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26) State an equation that can be written in the previous problem after making the first substitution.

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27) Solve the system of equations by using substitution. State the answer as an ordered pair.

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28) Solve the system of equations and state the answer as an ordered pair.

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29) Solve the system of equations and state the answer as an ordered pair.

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For the next two scenarios, define the variables for each unknown, write a system of equations, solve the system of equations, and then answer the questions that follow.

Scenario 1: Two eggs and three slices of bacon cost $5.25. One egg and two slices of bacon cost $3.25. What is the cost of one egg? What is the cost of one slice of bacon?

30) For Scenario 1 (a) define each of the variables and (b state two equations for the system of equations.

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31) What is the solution for the system of equations in the previous problem?

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Scenario 2: The cost to attend a basketball game is $3.00 for adults and $2.00 for students. There were 364 tickets sold at the game. If the sales for the tickets totaled $882, what was the number of adult tickets sold and the number of student tickets sold?

32) For Scenario 2 (a) define each of the variables and (b state two equations for the system of equations.

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33) What is the solution for the system of equations in the previous problem

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