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Solutions and Graphs of Systems of Equations and Inequalities

This review covers methods for solving various systems of equations and inequalities, including identifying solutions, no solutions, and maximization problems. Each problem requires different approaches to find coordinates, graph inequalities, and determine vertices of regions. Specific problems include finding solutions for linear systems with provided coordinates, evaluating conditions for maximum profit, and constructing objective functions to minimize costs for purchasing items. This comprehensive overview aids in mastering systems of equations in algebra.

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Solutions and Graphs of Systems of Equations and Inequalities

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  1. Ch 3 semester final review

  2. #1. Find the solution to the system (3, 0) (2, 3) O. (.5, 7.5)

  3. #2. Find the solution to the system B. No solutions D. (-5, 0) O. (11, -2)

  4. 3. Find the solution to the system (2, -3) (0, 9) All Real

  5. 4. Find the solution to the system No solution (-4, 1) (2, 0.333)

  6. #5. Find the solution to the system (0.67, 0) All real W. (0, - 4)

  7. #6. Find the solution to the system 3x + y = 4 -6x + 2y = 8 L . All reals R. No solution Z. (1, 1)

  8. #7. Find the solution to the system 6x + 2y = 7 Y = -3x + 9 Y. (0, 3.5) T. All reals M. No solutions

  9. #8. Find the solution to the system P. (1, 1, -2) Y. (.86, -.10, -.62) O. (1, -2, 0.5)

  10. #9. Graph the system of inequalities – show your solution area with a different color S R P

  11. #10. Graph the system of inequalities – show your solution area with a different color Y E H

  12. #11. Graph the system of inequalities – show your solution area with a different color S H B

  13. #12. Graph the system of inequalities – show your solution area with a different color B R V

  14. #13. Find the vertices of the graphed region L. (0,0), (-4, 5), (4, 0), (3, 2) E. (1, 0) (0,0) (0, 5) (3, 8) P. (0, 0) (5, 4) (0, -4) (0,5)

  15. 14. Maximize the statement:P(x,y) = $45x + $13y H. $1350 M. $1645 T. $1415

  16. #15. Find the constraints (the inequalities) for the question: Find the constraints (inequalities) if you want to maximize profit. H. 2x + 4y < 10 R. 2x + 4y < 50 T. 30x + 50y < 10 4x + 3y < 10 4x + 3y < 30 6x + 7y < 10

  17. #16. A shopper is buying x pounds of grapes and y pounds of cherries. Grapes cost $3/pound and cherries $8/pound. Write the objective function to find the minimum cost of purchasing grapes and cherries. O. Min = $11x + $11y Min = x + y L. Min = $3x + $8y

  18. What did one math book say to the other? ___ ____ ___ ___ ___ ___ ___ ___ ____ ____ ____ ___ ____ ____ ___ ___ ___ 2 1 12 14 11 1 14 15 13 9 7 13 3 12 13 4 1 ____ ____ ____ ___ ___ ___ ___ ___ ___ ___ ___ ___ ____ s. 14 7 10 1 5 12 8 9 1 11 6 7 8

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