MATH Basic Algebra I  - Unit 11: More Systems of Equations

The Elimination Method


1) Solve the system of equations using elimination. 

Hint:  Add the two equations to eliminate y.

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2)

Solve the system of equations using elimination. 

Hint:  Add the two equations to eliminate y.


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3)

Solve the system of equations using elimination. 

Multiply the top equation by –3, then add the two equations to eliminate x.


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Choosing a Method for Solving Systems

In the following problems, determine which method you would use to solve the system of equations using algebra, substitution or elimination, and then solve.


4)

What is a solution to this systems of equations?  What is the solution to the system of equations and what method did you use to solve?


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5)

What is the solution to the system of equations and what method did you use to solve?


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6)

What is the solution to the system of equations and what method did you use to solve?


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Consistent and Inconsistent Systems


7)

Explain the difference between a consistent and an inconsistent system. 


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8)

Solve the system and state whether it is consistent or inconsistent. 


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9)

Solve the system and state whether it is consistent or inconsistent. 


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10)

Solve the system and state whether it is consistent or inconsistent. 


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11)

Solve the system and state whether it is consistent or inconsistent. 


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12)

Which of the following is true about the graphs of the previous four systems of equations.  Click here to navigate to an online grapher, if needed.


Independent and Dependent Systems


13)

How many solutions does a dependent system have?


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14)

How many solutions does an independent system have?


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15)

Solve the system and state if it is independent or dependent. 


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16)

Solve the system and state if it is independent or dependent. 

Hint:  Move (1/2)x over to the right side of the equation, then add the two equations to eliminate x.         


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17) Which of the following is true about the graphs of the previous two systems of equations.  Click here to navigate to an online grapher, if needed.

Applications of Systems of Equations

In the following problems, (1) define variables for the unknown values, (2) write a system of equations, and then (3) solve. 

Refer to the following scenario for the next three problems.


18)

Define each of the variables. 


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19)

State the two equations for the system of equations. 


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20)

What is the solution for the system of equations? 


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Refer to the following scenario for the next three problems.


21)

Define each of the variables. 


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22)

State the two equations for the system of equations.


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23)

What is the solution for the system of equations? 


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Refer to the following scenario for the next three problems.


24) Define each of the variables. 

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25)

State the two equations for the system of equations.


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26)

What is the solution for the system of equations? 


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Review  


27)

Solve for y:  3y – 4 = 2y – 5

Click here to review the unit content explanation for Integers and Equations.


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Solve each inequality in the next two problems.


28)

Solve for x:  180 < 5x + 16

Click here to review the unit content explanation for Integers and Equations.


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29)

Solve for x:  2(2x – 5) > 90

Click here to review the unit content explanation for Integers and Equations.


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30)

Simplify the expression.

Click here to review the unit content explanation for Rational Numbers and Exponents


31)

Simplify the expression.

Click here to review the unit content explanation for Rational Numbers and Exponents


32)

Determine the domain and the range of the following relation:  {(–1, 3), (2, 3), (–1, 4), (2, 4)}.  Is this relation a function?

Click here to review the unit content explanation for Linear Functions.


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33)

Write an equation of the line in slope-intercept form that passes through the points (–2, 13) and (4, 7).

Click here to review the unit content explanation for Linear Equations and Graphs.


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