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Questions and Answers
What is the maximum amount of flour and cornmeal that can be purchased together given the budget constraint?
What is the maximum amount of flour and cornmeal that can be purchased together given the budget constraint?
Which inequality represents the condition that at least 6 pounds of flour and cornmeal are needed?
Which inequality represents the condition that at least 6 pounds of flour and cornmeal are needed?
What is the cost equation for the total amount spent on flour and cornmeal?
What is the cost equation for the total amount spent on flour and cornmeal?
Which ordered pair is a valid solution to the inequality system given?
Which ordered pair is a valid solution to the inequality system given?
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What graphing method is suggested to solve the system of inequalities?
What graphing method is suggested to solve the system of inequalities?
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What method is stated for solving the provided system of equations in Question 4?
What method is stated for solving the provided system of equations in Question 4?
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Which of the following equations is part of the system that needs to be solved in Question 2?
Which of the following equations is part of the system that needs to be solved in Question 2?
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What is the significance of using a scientific calculator as mentioned in the study guide?
What is the significance of using a scientific calculator as mentioned in the study guide?
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Which method could be used to solve the equations in Question 6?
Which method could be used to solve the equations in Question 6?
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In which scenario is it most appropriate to use the substitution method to solve a system of equations?
In which scenario is it most appropriate to use the substitution method to solve a system of equations?
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What does an ordered pair represent in the context of solving systems of equations?
What does an ordered pair represent in the context of solving systems of equations?
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How should responses be submitted after solving problems according to the study guide?
How should responses be submitted after solving problems according to the study guide?
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What is an example of an equation from the system provided in Question 5?
What is an example of an equation from the system provided in Question 5?
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What method can be used to solve the given system of equations -3x + y = -8 and -7x – y = -22?
What method can be used to solve the given system of equations -3x + y = -8 and -7x – y = -22?
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What is the perimeter of a rectangle if its length is defined as two inches more than three times the width and the perimeter is 40 inches?
What is the perimeter of a rectangle if its length is defined as two inches more than three times the width and the perimeter is 40 inches?
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If the cost difference between a large bag of chips and a small bag is $0.90, which equation best represents this scenario?
If the cost difference between a large bag of chips and a small bag is $0.90, which equation best represents this scenario?
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Which statement is correct regarding the system of equations -3x + y = -8 and -7x – y = -22?
Which statement is correct regarding the system of equations -3x + y = -8 and -7x – y = -22?
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What are the dimensions of the rectangle if its length is two inches more than three times the width and its perimeter is 40 inches?
What are the dimensions of the rectangle if its length is two inches more than three times the width and its perimeter is 40 inches?
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If 5 large bags and 3 small bags of chips cost a total of $17.22, what is the equation that represents this situation?
If 5 large bags and 3 small bags of chips cost a total of $17.22, what is the equation that represents this situation?
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What is the cost of a small bag of chips if 5 large bags and 3 small bags cost a total of $17.22?
What is the cost of a small bag of chips if 5 large bags and 3 small bags cost a total of $17.22?
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What is the total cost if you order 13 pizzas with cheese pizzas costing $7.50 each and pepperoni pizzas $8.50 each, totaling $101.50?
What is the total cost if you order 13 pizzas with cheese pizzas costing $7.50 each and pepperoni pizzas $8.50 each, totaling $101.50?
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What is the total cost of 3 pairs of jeans and 6 shirts if their combined price is $104.25?
What is the total cost of 3 pairs of jeans and 6 shirts if their combined price is $104.25?
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If scarves take 2 hours to knit and sweaters take 10 hours, how many total items can Mary knit in a maximum of 40 hours if she knits at least 5 items per week?
If scarves take 2 hours to knit and sweaters take 10 hours, how many total items can Mary knit in a maximum of 40 hours if she knits at least 5 items per week?
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Which correctly describes the relationship between multiple-choice problems and word problems in terms of quantity?
Which correctly describes the relationship between multiple-choice problems and word problems in terms of quantity?
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What would be the result of graphing the inequality $y \geq 2x - 4$?
What would be the result of graphing the inequality $y \geq 2x - 4$?
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How much more does the cost of 4 pairs of jeans and 5 shirts ($112.15) exceed the cost of 3 pairs of jeans and 6 shirts ($104.25)?
How much more does the cost of 4 pairs of jeans and 5 shirts ($112.15) exceed the cost of 3 pairs of jeans and 6 shirts ($104.25)?
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What is the nature of the system of inequalities represented by Mary's knitting time that limits her to 40 hours and at least 5 items?
What is the nature of the system of inequalities represented by Mary's knitting time that limits her to 40 hours and at least 5 items?
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What information does the inequality $3x + 4y < 16$ provide about the relationship between x and y?
What information does the inequality $3x + 4y < 16$ provide about the relationship between x and y?
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If Mary knits 5 scarves and 5 sweaters, how many hours will she have spent knitting?
If Mary knits 5 scarves and 5 sweaters, how many hours will she have spent knitting?
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Flashcards
System of Inequalities
System of Inequalities
A set of two or more inequalities with the same variables.
Graphing Inequalities
Graphing Inequalities
The process of drawing the graph corresponding to an inequality.
Solution Set
Solution Set
All possible solutions that satisfy the inequalities.
Ordered Pair
Ordered Pair
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Testing Solutions
Testing Solutions
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Systems of Equations
Systems of Equations
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Substitution Method
Substitution Method
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Elimination Method
Elimination Method
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Graphing Method
Graphing Method
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Solution to a System
Solution to a System
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Inequalities in Systems
Inequalities in Systems
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Scientific Calculator Use
Scientific Calculator Use
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Number of Solutions
Number of Solutions
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Perimeter of a Rectangle
Perimeter of a Rectangle
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Define Your Variables
Define Your Variables
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Cost Equation from Chips Problem
Cost Equation from Chips Problem
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Pizza Cost Equation
Pizza Cost Equation
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Variables Definition
Variables Definition
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Inequality
Inequality
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Cost of Jeans and Shirts
Cost of Jeans and Shirts
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Word Problems
Word Problems
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Knitting Constraints
Knitting Constraints
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Linear Inequalities System
Linear Inequalities System
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Study Notes
Unit 5 Study Guide: Systems of Equations & Inequalities
- Solving systems algebraically: Solve problems using algebraic methods like substitution or elimination. Submit answers through Formative for feedback. Multiple submissions are allowed before the test and can improve scores. Using a scientific calculator is permitted, but graphing calculators are not.
Question 1: Graphing a System of Equations
- A graph displays a system of equations. Students need to identify the solution to this system from the provided graph.
Question 2: Plotting the Solution
- Find the solution point for the system of equations
y = -6and3x – 3y = 9by plotting on the graph.
Question 3: Substitution Method
- Solve the system of equations
-4x + 5y = 27andx - 6y = -2using the substitution method.
Question 4: Elimination Method
- Solve the system of equations
-6x + 6y = 30and-2x - 5y = -18using the elimination method. Express the solution as an ordered pair (x, y).
Question 5: Substitution or Elimination (System 1)
- Solve the system of equations
y = 2xandy = 9x – 7using either the substitution or elimination method.
Question 6: Substitution or Elimination (System 2)
- Solve the system of equations
-3x + y = -8and-7x - y = -22using either the substitution or elimination method.
Question 7: Graphing Method
- Solve the system of equations
x – y = 4and2x – y = 2using the graphing method.
Question 8: Substitution or Elimination (System 3)
- Solve the system of equations
x/5 + y/10 = 6andx/10 + 3y/5 = 5using either the substitution or elimination method. Include a graphing solution method.
Question 9: Systems Solution Type
- Solve the system of equations
-4x + 3y = 6andy = x – 5. Determine if the solution is one, infinitely many or no solution.
Question 10: Number of Solutions (Multiple Systems)
- Count the number of solutions for each presented system of equations graphically.
Question 11: System of Equations (Rectangle)
- Create and solve a system of equations concerning a rectangle's perimeter and dimensions. Define the variables first.
Question 12: System of Equations (Chips)
- Create and solve a system of equations related to the cost of bags of chips. Define the variables first.
Question 13: System of Equations (Algebra Test)
- Create and solve a system of equations concerning a 100-point algebra test. The test contains multiple choice and word problems. Define the variables first
Question 14: System of Equations (Jeans and Shirts)
- Create and solve a system of equations related to the cost of pairs of jeans and shirts. Define the variables first.
Question 15: System of Equations (Pizzas)
- Create and solve a system of equations about purchasing different types of pizzas for a class party.
Question 16: Graphing Inequality
- Graph the inequality
y > x + 2
Question 17: Inequality from Graph
- Determine the inequality represented by the given graph.
Question 18: System of Inequalities (Knitting)
- Create and solve a system of inequalities about knitting scarves and sweaters, considering time constraints and desired output. Define variables first.
Question 19: Graphing System of Inequalities
- Graph and identify the solutions to the system of inequalities:
y ≥ 2x - 4and3x + 4y < 16.
Question 20: Identifying Inequalities from a Graph
- Identify the system of inequalities represented by the given graph.
Question 21: Systems of Inequalities (Flour and Cornmeal)
- Solve a word problem involving systems of inequalities related to purchasing flour and cornmeal for tortillas.
Question 22: Checking Ordered Pairs in Inequalities
- Determine if an ordered pair is a solution to a given system of inequalities.
Question 23: Solving Linear Inequalities Graphically
- Graph and solve a system of linear inequalities. Graphically determine the solution region.
Question 24: Solution Set for Inequalities
- Identify the points within a graphically solution set of two linear inequalities.
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Description
This study guide focuses on solving systems of equations and inequalities using various methods. Students will explore graphing solutions, substitution, and elimination techniques. Practice problems are provided to strengthen understanding and application of these algebraic methods.
