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Systems of Inequalities and Linear Equations

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Systems of Inequalities and Linear Equations

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Questions and Answers

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?

$-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?

6 (correct)

What is the relationship between peanut butter and oatmeal raisin cookies sold as derived from the problem statement?

<p>P = O + 20</p> Signup and view all the answers

Which of the following represents an equation that accurately describes three variables with their respective coefficients?

<p>$2x + 3y + z = 14$</p> Signup and view all the answers

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.