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Exploring Solutions to Linear Systems: Algebraic Approach and Graphical Analysis

This mini-review focuses on solving and graphing linear systems to determine the number of solutions they possess. It includes examples such as (y = x + 1) and (y = -x + 3), concluding with a unique solution at (1, 2). The review also covers systems with infinitely many solutions and demonstrates the algebraic checks for different scenarios. Additionally, it discusses practical applications in wage determination and fundraising pledges, providing insight into the real-world implications of linear systems.

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Exploring Solutions to Linear Systems: Algebraic Approach and Graphical Analysis

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  1. Ch. 3 Mini Review

  2. Graph the linear system and tell how many solutions it has. If there is exactly one solution, estimate the solution and check it algebraically. y= x + 1 y = -x + 3

  3. The solution is(1, 2)

  4. Graph the linear system and tell how many solutions it has. If there is exactly one solution, estimate the solution and check it algebraically. X + 2y = -2 -3x -6y = 6

  5. There are infinitely many solutions

  6. Solve the System x + y = 2 y = 2x + 5

  7. (-1, 3)

  8. Solve the System y – 2x = -5 y – x = -3

  9. (2, -1)

  10. Solve the System 2x – y = -8 2x + y = 4

  11. (-1, 6)

  12. Solve the System x + 4y + z = 12 y – 3z = -7 z = 3

  13. (1, 2, 3)

  14. Solve the System x + y + 2z = 5 x + 2y + z = 8 2x + 3y – z = 1

  15. (-7, 6, 3)

  16. Solve the System 2x – y = 9 5x + 2y = 27

  17. (5, 1)

  18. Solve the System 3x + 5y = 8 4x + 7z = 18 y + z = 3

  19. (1, 1, 2)

  20. Graph the system of linear inequalities y ≤ 2 x > 3

  21. Graph the system of linear inequalities x ≥ 0 y ≥ 0 2x + y ≤ 4

  22. Earning moneyYou work at a grocery store. Your hourly wage is greater after 6:00 p.m. than it is during the day. One week you work 20 daytime hours and 20 evening hours and earn $280. Another week you work 30 day time hours and 12 evening hours and earn a total of $276. What is your daytime rate? What is your evening rate?

  23. daytime = $6 evening = $8

  24. TelethonDuring a recent telethon, people pledged $25 or $50. Twice as many people pledged $25 as $50. Altogether, $18,000 was pledged. How many people pledged $25?

  25. 360

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