Podcast
Questions and Answers
What are the quantities of each type of cookie sold at the bakery?
What are the quantities of each type of cookie sold at the bakery?
- C: 100, O: 70, P: 90
- C: 130, O: 50, P: 70
- C: 120, O: 60, P: 80
- C: 110, O: 55, P: 75 (correct)
Which inequality represents a relationship where the slope of the line is negative and the region below the line is shaded?
Which inequality represents a relationship where the slope of the line is negative and the region below the line is shaded?
- $-y ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ }). $-2x + y + 2z = -3$
- $x + 2y ≤ 8$ (correct)
- $x - y ≥ 3$
- $3x - y > 5$
In the equation $2x + y - z = 8$, if x = 2 and z = 4, what is the value of y?
In the equation $2x + y - z = 8$, if x = 2 and z = 4, what is the value of y?
- 6 (correct)
- 8
- 4
- 0
What is the relationship between peanut butter and oatmeal raisin cookies sold as derived from the problem statement?
What is the relationship between peanut butter and oatmeal raisin cookies sold as derived from the problem statement?
Which of the following represents an equation that accurately describes three variables with their respective coefficients?
Which of the following represents an equation that accurately describes three variables with their respective coefficients?
Flashcards
System of Inequalities
System of Inequalities
A system of inequalities is a set of two or more inequalities that share the same variables. A solution to a system of inequalities must satisfy all inequalities in the system. The solution set is the set of all points that satisfy all the inequalities.
Solving Systems of Linear Equations with Three Variables
Solving Systems of Linear Equations with Three Variables
To solve a system of linear equations with three variables, you need to find the values of x, y, and z that satisfy all three equations. One useful strategy is elimination, where you manipulate the equations to eliminate one variable at a time.
Graphing Systems of Inequalities
Graphing Systems of Inequalities
When graphing a system of inequalities, the solution set is represented by the shaded region where all the inequalities overlap. A solid line means the line itself is included in the solution, while a dashed line means it is not.
Real-world applications of inequalities
Real-world applications of inequalities
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Elimination Method
Elimination Method
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Study Notes
Systems of Inequalities
- Graph inequalities by graphing the related equations first, and then shade the appropriate region of the coordinate plane.
- Dashed lines indicate "less than" or "greater than"
- Solid lines indicate "less than or equal to" or "greater than or equal to"
Systems of Linear Equations with Three Variables
- A bakery sells three types of cookies: chocolate chip, oatmeal raisin, and peanut butter.
- A total of 240 cookies were sold.
- Chocolate chip cookies sold were twice the number of oatmeal raisin cookies.
- Peanut butter cookies sold were 20 more than the number of oatmeal raisin cookies.
- Variables: C = chocolate chip, O = oatmeal raisin, P = peanut butter
- Equations: C + O + P = 240, C = 2O, P = O + 20
- Solving the system of equations gives: C = 110, O = 55, P = 75
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Description
This quiz covers graphing systems of inequalities and solving systems of linear equations with three variables. You will learn to represent inequalities on the coordinate plane and apply algebraic methods to solve real-world problems involving cookie sales in a bakery. Test your understanding of these fundamental concepts in algebra.
