Tuesday, May 21, 2024

# Algebra 1 Chapter 5 Cumulative Review

## Big Ideas Math Book Algebra 1 Answer Key Chapter 5 Solving Systems Of Linear Equations

Algebra 1 Final Exam Giant Review

We have covered all the Questions from Exercises, Chapter Tests, Review Tests, Quiz, Assessment Tests, Cumulative Assessments, etc. in the Solving Systems of Linear Equations Big Ideas Math Algebra 1 Answer Key. You can understand the topics in it easily as they are explained in an elaborate manner keeping in mind your level of understanding.

## Solving Systems Of Linear Equations Cumulative Assessment

Question 1.The graph of which equation is shown?Answer:

Question 2.A van rental company rents out 6-, 8-, 12-, and 16-passenger vans. The function C = 100 + 5x represents the cost C of renting an x-passenger van for a day. Choose the numbers that are in the range of the function.Answer:

Question 3.Fill in the system of linear inequalities with < , , > , or so that the graph represents the system.Answer:

Question 4.Your friend claims to be able to fill in each box with a constant so that when you set each side of the equation equal to y and graph the resulting equations, the lines will intersect exactly once. Do you support your friends claim? Explain.Answer:

Question 5.Select the phrases you should use when describing the transformations from the graph of f to the graph of g.Answer:

Which two equations form a system of linear equations that has no solution?Answer:

Question 7.Fill in a value for a so that each statement is true for the equation ax 8 = 4 x.Answer:

Which ordered pair is a solution of the linear inequality whose graph is shown?Answer:

Which of the systems of linear equations are equivalent?Answer:

Question 10.The value of x is more than 9. Which of the inequalities correctly describe the triangle? The perimeter is represented by P, and the area is represented by A.Answer:

## Solving Systems Of Linear Equations Chapter Review

5.1 Solving Systems of Linear Equations by Graphing

Solve the system of linear equations by graphing.Question 1.

x + y < 1 5x + y > 4Answer:

y \x + 1-3x + y > -2Answer:

Question 12.You pay \$45.50 for 10 gallons of gasoline and 2 quarts of oil at a gas station. Your friend pays \$22.75 for 5 gallons of the same gasoline and 1 quart of the same oil.a. Is there enough information to determine the cost of 1 gallon of gasoline and 1 quart of oil? Explain.b. The receipt shown is for buying the same gasoline and same oil. Is there now enough information to determine the cost of 1 gallon of gasoline and 1 quart of oil? Explain.c. Determine the cost of 1 gallon of gasoline and 1 quart of oil.Answer:

Question 14.You have at most \$60 to spend on trophies and medals to give as prizes for a contest.a. Write and graph an inequality that represents the numbers of trophies and medals you can buy. Identify and interpret a solution of the inequality.b. You want to purchase at least 6 items. Write and graph a system that represents the situation. How many of each item can you buy?Answer:

Question 15.Compare the slopes and y-intercepts of the graphs of the equations in the linear system 8x + 4y = 12 and 3y = -6x 15 to determine whether the system has one solution, no solution, or infinitely many solutions. Explain.Answer:

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## Solving Systems Of Linear Equations By Substitution 52 Exercises

Vocabulary and Core Concept CheckQuestion 1.Describe how to solve a system of linear equations by substitution.Answer:

Question 2.NUMBER SENSEWhen solving a system of linear equations by substitution, how do you decide which variable to solve for in Step 1?Answer:

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In Exercises 38, tell which equation you would choose to solve for one of the variables. Explain.Question 3.

Question 17.ERROR ANALYSISDescribe and correct the error in solving for one of the variables in the linear system 8x + 2y = -12 and 5x y = 4.Answer:

Question 18.ERROR ANALYSISDescribe and correct the error in solving for one of the variables in the linear system 4x + 2y = 6 and 3x + y = 9.Answer:

Question 19.MODELING WITH MATHEMATICSA farmer plants corn and wheat on a 180-acre farm. The farmer wants to plant three times as many acres of corn as wheat. Write a system of linear equations that represents this situation. How many acres of each crop should the farmer plant?Answer:

Question 20.MODELING WITH MATHEMATICSA company that offers tubing trips down a river rents tubes for a person to use and cooler tubes to carry food and water. A group spends \$270 to rent a total of 15 tubes. Write a system of linear equations that represents this situation. How many of each type of tube does the group rent?Answer:

In Exercises 2124, write a system of linear equations that has the ordered pair as its solution.Question 21.

Find the sum or difference.Question 36.

## Lesson 55 Solving Equations By Graphing

Essential Question How can you use a system of linear equations to solve an equation with variables on both sides?

Previously, you learned how to use algebra to solve equations with variables on both sides. Another way is to use a system of linear equations.

EXPLORATION 1

Solving an Equation by GraphingWork with a partner. Solve 2x 1 = \ x + 4 by graphing.a. Use the left side to write a linear equation. Then use the right side to write another linear equation.b. Graph the two linear equations from part . Find the x-value of the point of intersection. Check that the x-value is the solution of2x 1 = \x + 4.c. Explain why this graphical method works.

EXPLORATION 2

Solving Equations Algebraically and GraphicallyWork with a partner. Solve each equation using two methods.Method 1 Use an algebraic method.Method 2 Use a graphical method.Is the solution the same using both methods?a. \x + 4 = \x + 1b. \x + 4 = \x + 3c. \ x 1 = \x 4d. \ x + \ = 3x 3e. -x + 2.5 = 2x 0.5f. 3x + 1.5 = x + 1.5

Question 3.How can you use a system of linear equations to solve an equation with variables on both sides?Answer:

Question 4.Compare the algebraic method and the graphical method for solving a linear equation with variables on both sides. Describe the advantages and disadvantages of each method.Answer:

Solve the equation by graphing. Check your solution.Question 1.\x 3 = 2xAnswer:

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## Lesson 52 Solving Systems Of Linear Equations By Substitution

Essential Question How can you use substitution to solve a system of linear equations?

EXPLORATION 1

Using Substitution to Solve SystemsWork with a partner. Solve each system of linear equations using two methods.Method 1 Solve for x first.Solve for x in one of the equations. Substitute the expression for x into the other equation to find y. Then substitute the value of y into one of the original equations to find x.

Method 2 Solve for y first.Solve for y in one of the equations. Substitute the expression for y into the other equation to find x. Then substitute the value of x into one of the original equations to find y.Is the solution the same using both methods? Explain which method you would prefer to use for each systema. x + y = -7

Writing and Solving a System of EquationsWork with a partner.a. Write a random ordered pair with integer coordinates. One way to do this is to use a graphing calculator. The ordered pair generated at the right is .b. Write a system of linear equations that has your ordered pair as its solution.c. Exchange systems with your partner and use one of the methods from Exploration 1 to solve the system. Explain your choice of method.

How can you use substitution to solve a system of linear equations?Answer:

Question 4.Use one of the methods from Exploration 1 to solve each system of linear equations. Explain your choice of method. Check your solutions.a. x + 2y = -7

## Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems Of Linear Equations

If you are searching for instant help on the concepts of Algebra 1 Ch 5 Solving Systems of Linear Equations then this is the one-stop destination for all your needs. Make the most out of the BIM Book Algebra 1 Chapter 5 Solving Systems of Linear Equations Solutions Key provided and clarify your doubts on the same. You need not worry about the accuracy of the Solving Systems of Linear Equations Big Ideas Math Algebra 1 Answers Chapter 5 as they are given to you by subject experts.

To make it easy for you we have compiled the Big Ideas Math Algebra 1 Answers for Chapter 5 Textbook Questions via quick links available here. You can tap on them or download them free of cost and prepare effectively. Practice the BIM Textbook Algebra 1 Ch 5 Solving Systems of Linear Equations Answers on a regular basis so that your speed and accuracy will be improved in the actual exams.

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## Systems Of Linear Inequalities 57 Exercises

Vocabulary and Core Concept CheckQuestion 1.VOCABULARYHow can you verify that an ordered pair is a solution of a system of linear inequalities?Answer:

Question 2.WHICH ONE DOESNT BELONG?Use the graph shown. Which of the ordered pairs does not belong with the other three? Explain your reasoning.Answer:

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In Exercises 36, tell whether the ordered pair is a solution of the system of linear inequalities.Question 3.

Question 29.MODELING WITH MATHEMATICSYou can spend at most \$21 on fruit. Blueberries cost \$4 per pound, and strawberries cost \$3 per pound. You need at least 3 pounds of fruit to make muffins.a. Write and graph a system of linear inequalities that represents the situation.b. Identify and interpret a solution of the system.c. Use the graph to determine whether you can buy 4 pounds of blueberries and 1 pound of strawberries.Answer:

Question 30.MODELING WITH MATHEMATICSYou earn \$10 per hour working as a manager at a grocery store. You are required to work at the grocery store at least 8 hours per week. You also teach music lessons for \$15 per hour. You need to earn at least \$120 per week, but you do not want to work more than 20 hours per week.a. Write and graph a system of linear inequalities that represents the situation.b. Identify and interpret a solution of the system.c. Use the graph to determine whether you can work 8 hours at the grocery store and teach 1 hour of music lessons.Answer:

Mathematical Practices

## Lesson 51 Solving Systems Of Linear Equations By Graphing

Advanced Algebra 4 5 4 8 Study Guide Cumulative Review

Essential Question How can you solve a system of linear equations?

EXPLORATION 1

Writing a System of Linear EquationsWork with a partner. Your family opens a bed-and-breakfast. They spend \$600 preparing a bedroom to rent. The cost to your family for food and utilities is \$15 per night. They charge \$75 per night to rent the bedroom.a. Write an equation that represents the costs.b. Write an equation that represents the revenue .c. A set of two linear equations is called a system of linear equations. Write the system of linear equations for this problem.

EXPLORATION 2

Using a Table or Graph to Solve a SystemWork with a partner. Use the cost and revenue equations from Exploration 1 to determine how many nights your family needs to rent the bedroom before recovering the cost of preparing the bedroom. This is the break-even point.a. Copy and complete the table.b. How many nights does your family need to rent the bedroom before breaking even?c. In the same coordinate plane, graph the cost equation and the revenue equation from Exploration 1.d. Find the point of intersection of the two graphs. What does this point represent? How does this compare to the break-even point in part ? Explain.

How can you solve a system of linear equations? How can you check your solution?Answer:

Question 4.Solve each system by using a table or sketching a graph. Explain why you chose each method. Use a graphing calculator to check each solution.a. y = -4.3x 1.3

## Algebra Terms 2 And 4

Term 2/4 Calendar ClickHERE

ASSIGNMENTS:

All assignments are listed on the Term Calendar for Term 2/4 shown above.

CHAPTER 7 Solving Systems of Equations

7.1 Solve a Linear System of Equations by Graphing Investigation Click HERE

7.2 Solve a Linear System of Equations by Substitution Partner Coach Click HERE

CHAPTER 8 Properties of Exponents

CUMULATIVE REVIEW Chapters 7 and 8

CHAPTER 10 Quadratic Equations: Graphing and Solving

## Solving Equations By Graphing 55 Exercises

Vocabulary and Core Concept CheckQuestion 1.REASONINGThe graphs of the equations y = 3x 20 and y = -2x + 10 intersect at the point . Without solving, find the solution of the equation 3x 20 = -2x + 10.Answer:

Question 2.WRITINGExplain how to rewrite the absolute value equation |2x 4| = |-5x + 1| as two systems of linear equations.Answer:

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In Exercises 36, use the graph to solve the equation. Check your solution.Question 3.

Question 33.MODELING WITH MATHEMATICSYou need to hire a catering company to serve meals to guests at a wedding reception. Company A charges \$500 plus \$20 per guest. Company B charges \$800 plus \$16 per guest. For how many guests are the total costs the same at both companies?Answer:

Question 34.MODELING WITH MATHEMATICSYour dog is 16 years old in dog years. Your cat is 28 years old in cat years. For every human year, your dog ages by 7 dog years and your cat ages by 4 cat years. In how many human years will both pets be the same age in their respective types of years?Answer:

Question 35.MODELING WITH MATHEMATICSYou and a friend race across a field to a fence and back. Your friend has a 50-meter head start. The equations shown represent you and your friends distances d from the fence t seconds after the race begins. Find the time at which you catch up to your friend.You: d = |-5t + 100|Your friend: d = |-3\t + 50|Answer:

f = -2x + 1 g = fAnswer:

f = \x 2 g = fAnswer:

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## Algebra 1 Teacher’s Edition With Cd

The Algebra 1 Teachers Edition contains the student pages with overprint answers as well as solutions for exercises and additional math problems. Teachers will find the one-on-one activities, presentation suggestions, and common student errors features to be helpful resources. This edition also gives suggested assignments, and schedules are given for three tracksminimum, standard, and extended. The CD that accompanies the Teachers Edition has Projection Ready Answers, Mathardy and Visuals.

## Solving Systems Of Linear Equations 5154 Quiz

Use the graph to solve the system of linear equations. Check your solution.Question 1.y = \x + 2y = x 2

Question 13.You plant a spruce tree that grows 4 inches per year and a hemlock tree that grows 6 inches per year. The initial heights are shown.a. Write a system of linear equations that represents this situation.b. Solve the system by graphing. Interpret your solution.Answer:

Question 14.It takes you 3 hours to drive to a concert 135 miles away. You drive 55 miles per hour on highways and 40 miles per hour on the rest of the roads.a. How much time do you spend driving at each speed?b. How many miles do you drive on highways? the rest of the roads?Answer:

Question 15.In a football game, all of the home teams points are from 7-point touchdowns and 3-point field goals. The team scores six times. Write and solve a system of linear equations to find the numbers of touchdowns and field goals that the home team scores.Answer:

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## Lesson 56 Graphing Linear Inequalities In Two Variables

Essential Question How can you graph a linear inequality in two variables?A solution of a linear inequality in two variables is an ordered pair that makes the inequality true. The graph of a linear inequality in two variables shows all the solutions of the inequality in a coordinate plane.

EXPLORATION 1

Writing a Linear Inequality in Two VariablesWork with a partner.a. Write an equation represented by the dashed line.b. The solutions of an inequality are represented by the shaded region. In words, describe the solutions of the inequality.c. Write an inequality represented by the graph. Which inequality symbol did you use? Explain your reasoning.

EXPLORATION 2

Using a Graphing CalculatorWork with a partner. Use a graphing calculator to graph y \x 3.a. Enter the equation y = \x 3 into your calculator.b. The inequality has the symbol . So, the region to be shaded is above the graph of y = \x 3, as shown. Verify this by testing a point in this region, such as , to make sure it is a solution of the inequality.Because the inequality symbol is greater than or equal to, the line is solid and not dashed. Some graphing calculators always use a solid line when graphing inequalities. In this case, you have to determine whether the line should be solid or dashed, based on the inequality symbol used in the original inequality

EXPLORATION 3