Graphing Systems of Equations
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| 1) Complete the following sentence: Two equations in two variables are called a __________.
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| 2) List the three types of possible solutions to a system of equations.
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| 3) Describe the graph of an equation’s lines when a system of equation has no solution. Explain why there is no solution.
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In the following questions, graph each system of equations on graph paper, and then state the solution to the system of equations.
Click here to view and print graph paper.
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| 4) What is the solution to the system of equations?
Hint: Solve each equation for y first, then graph.
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| 5) What is the solution to the system of equations?
Hint: Solve each equation for y first, then graph.
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| 6) Explain how to solve the previous problem.
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| 7) What is the solution to the system of equations?
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| 8) What is the solution to the system of equations?
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Solving Systems by Substitution
In the following problems, use the substitution method to solve the systems of equations. State the solution as an ordered pair if there is one solution. If there are no solutions, state "No Solution." If there are many solutions, state "Many Solutions."
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| 9) Solve by using substitution and state the solution as an ordered pair. Show all of the steps used to determine the solution.
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| 10) Solve by using substitution and state the solution as an ordered pair.
Hint: Solve one of the equations for y first.
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| 11) Solve by using substitution and state the solution as an ordered pair.
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| 12) Solve by using substitution.
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| 13) Solve by using substitution.
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| 14) Solve by using substitution.
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| 15) A rancher raises five times as many cows as horses. If he has 168 cows and horses, how many cows does he have? Complete the equations shown below, and then use substitution to solve.
Let c represent the number of cows and h represent the number of horses.
Equation 1: c = __h
Equation 2: c + h = __
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19) Translate the following phrase into an algebraic expression: "twice the quantity of the sum of a number and 6."
Click here to review the unit content explanation for Expressions, Variables, and Properties. |
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| 20) Translate the following phrase into an algebraic expression: "the product of n and 7 divided by 16."
Click here to review the unit content explanation for Expressions, Variables, and Properties.
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| 21) What property is illustrated in the following expression: a(1) = a
Click here to review the unit content explanation for Expressions, Variables, and Properties.
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| 22) What property is illustrated in the following expression: (x + 4) + y = x + (4 + y)
Click here to review the unit content explanation for Expressions, Variables, and Properties.
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| 26) Simplify the expression by applying the laws of exponents.
Click here to review the unit content explanation for Rational Numbers and Exponents.
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| 27) Simplify the following terms by applying the distributive property and combining like terms: 8(x – 2) + 7x + 6y – 3
Click here to review the unit content explanation for Polynomials.
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| 28) Explain the mistake made in simplifying the problem below.
Click here to review the unit content explanation for Polynomials.
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| 29) Tommy takes his dog Em for a walk after school. Which scenario is represented best by the graph in terms of Tommy and Em's walk and rate of change?
Click here to review the unit content explanation for Linear Functions.
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| 30) Mr. and Mrs. Bondy need to rent a car to take their children on a vacation. The table below shows the price list for renting a mid-size car for several days.
(a) Write an equation in slope-intercept form that correctly describes the relationship between the number of days and the rental charge.
(b) How much will it cost to rent the car for 14 days?
(c) If the family spent $1150 for renting the car, how many days did they rent the car?
Click here to review the unit content explanation for Linear Equations and Graphs.
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| 31) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form. |
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