Inequalities Test - Study Notes
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Questions and Answers

Which ordered pair satisfies the inequality $y < 2x - 1$ and $x + 4y \leq 8$?

  • (4, 2)
  • (-1, 1)
  • (2, 3)
  • (3, 1) (correct)

    • What is the correct ordered pair that meets the conditions $y \geq x$ and $2x - y \geq 3$?

  • (5, 0)
  • (2, 1)
  • (0, 4) (correct)
  • (3, 1)

    • Identify the ordered pair that meets the condition $x \geq 2$ and satisfies the system $8s + 4c \leq 120$ and $8s + 4c > 120$.

  • (2, 3)
  • (4, 5) (correct)
  • (3, 2)
  • (2, 8)

    • Which combination could Jacie purchase while satisfying the criteria for chicken?

    <p>10 pounds of steak and 11 pounds of chicken (A)</p> Signup and view all the answers

    Which of the following ordered pairs does not satisfy both inequalities in the system presented?

    <p>(1, 0) (D)</p> Signup and view all the answers

    Which inequality represents a linear constraint that includes the point (0, 1)?

    <p>2x + y &lt; 3 (C)</p> Signup and view all the answers

    What is the solution to the system of equations represented by y = 3x - 1 and y = 2x - 5?

    <p>(1, 2) (B)</p> Signup and view all the answers

    Which ordered pair satisfies the inequality 5x + 2y < 6?

    <p>(-1, 1) (D)</p> Signup and view all the answers

    Which linear inequality corresponds to the graph where the boundary line is y = 2x - 3 and shaded below?

    <p>y &lt; 2x - 3 (C)</p> Signup and view all the answers

    What is the correct expression for the system of equations represented by x + 2y = 5 and y = 3?

    <p>(2, 3) (C)</p> Signup and view all the answers

    Which inequality is represented by the graph that has a shaded area above the line y = -2x - 3?

    <p>y &gt; -2x - 3 (C)</p> Signup and view all the answers

    For the equation 6x - 3y = 12, which points are solutions?

    <p>(2, 0) (C)</p> Signup and view all the answers

    In which option does the graph represent the inequality x + 4y ≤ 8 accurately?

    <p>The line intersects the y-axis at (0, 2) (A)</p> Signup and view all the answers

    Flashcards

    Ordered Pair

    A pair of numbers, usually represented as (x, y), that indicate a point on a graph.

    Linear Inequality

    An inequality that describes a region of the coordinate plane where one variable is greater or less than a linear expression.

    Graphing Inequalities

    The process of drawing the regions represented by inequalities on a coordinate plane.

    Feasible Region

    The area on a graph where all constraints of a system of inequalities are satisfied.

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    Solution to an Inequality

    An ordered pair that makes the inequality true when substituted into it.

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    System of equations

    A set of two or more equations with the same variables.

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    Graphing method

    A method to solve equations by plotting them on a graph.

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    Substitution method

    A method for solving a system of equations by replacing one variable.

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    Elimination method

    A method that eliminates one variable to solve a system of equations.

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    Study Notes

    Inequalities Test - Study Notes

    • Part 1: Free Response - Graphing Systems of Equations

    • Determine the solution for each graph by identifying the intersection point of the lines.

    • Record answers in the answer column.

    • Part 2: Solving Systems of Equations - Multiple Choice

    • Question 9: Select the linear inequality that matches the given graph.

    • Question 10: Select the linear inequality that matches the given graph.

    • Question 11: Determine which ordered pair is a solution to the given inequality 5x + 2y < 6.

    • Part 3: Systems of Linear Inequalities (Graphing)

    • Question 12: Graph the system of linear inequalities and determine which ordered pair is a solution. The system is y < 2x - 1 and x + 4y ≤ 8.

    • Question 13: Graph the system of linear inequalities and determine which ordered pair is a solution. The system is y ≤ (1/2)x and 2x - y ≥ 3.

    • Question 14: Algebraically determine which ordered pair is a solution to the system of inequalities. x ≥ 2 and x + y < 4.

    • Part 4: Word Problems

    • Question 15: A rectangle's length is 9 inches longer than its width, and its perimeter is 46 inches. Determine the system of equations that models this scenario.

    • Question 16: Clay has 10 more magnatiles than 3 times as many as Bennett. Together, they have 70 magnatiles. Determine the system of equations to find the number of magnatiles each has.

    • Question 17: Jacie is buying steak and chicken. She needs at least 20 pounds of meat and wants to spend at most $120. Steak is $8 per pound and chicken is $4 per pound. Determine the inequalities to represent these constraints.

    • Question 18: Given the situation in question 17, identify a possible combination of steak and chicken purchases.

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    Related Documents

    Systems of Equations & Inequalities Test B PDF

    Description

    This quiz focuses on graphing systems of equations and solving linear inequalities. It includes free response questions, multiple choice sections, and graphing challenges to assess understanding of linear inequalities and their intersections. This assessment is ideal for students preparing for tests on inequalities and systems of equations.

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