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Solve Linear Systems Graphically & Algebraically

Learn how to find solutions to systems of linear equations by graphing or using algebraic methods such as substitution and elimination. Practice problems included for better understanding.

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Solve Linear Systems Graphically & Algebraically

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  1. Find the solution to the system graphically. y = -3x + 2 y = 2x – 3

  2. Algebra II 3.1: Solve Linear Systems by Graphing Practice (no hw): p.156 (3, 4, 8, 9, 11) Quiz 3.1-3.2: Wednesday – 11/6

  3. How to solve linear systems graphically. • Graph both lines in the same coordinate plane. • Your solution is the ordered pair where the two lines intersect. • What would be the solution if the lines do not intersect? • What would be the solution if the lines overlap each other?

  4. Find the solution to the system graphically. y = 2 x = -4

  5. Find the solution to the system graphically. y = -3x – 2 3x + 2y = 2

  6. Find the solution to the system graphically. 2x + y = 4 -4x - 2y = -2

  7. Find the solution to the system graphically. y = -1 3x + y = 5

  8. Do Now: Find the solution to the system graphically. x – 7y = 7 -3x + 21y = -42

  9. Algebra II 3.2: Solve Linear Systems Algebraically HW: p.164 (4-14 even) Quiz 3.1, 3.2: Wednesday, 11/6

  10. What are the two algebraic methods of solving a system of equations? • Substitution • Elimination (linear combinations)

  11. 3.2 B: Solve the system using substitution 1.) x + 2y = 6 3x – 2y = 2

  12. Solve the system using substitution 2.) 6x – 2y = 5 -3x + y = 7

  13. 3.2 B: Solve the system using substitution 3.) x + 3y = 3 2x – 4y = 6

  14. p.162 Example 3 To raise money for uniforms, your school sells t-shirts. Short sleeve t-shirts cost $5 each and are sold for $8 each. Long sleeve t-shirts cost the school $7 each and are sold for $12 each. The school spends a total of $2500 on t-shirts and sells all of them for $4200. How many short sleeve t-shirts are sold?

  15. p.165 # 55 In one week, a music store sold 9 guitars for a total of $3611. Electric guitars sold for $479 each and acoustic guitars sold for $339 each. How many type of each guitar were sold?

  16. Solve the system using substitution 4.) 3x – y = 2 6x + 3y = 14

  17. 3.2 B: Solve the system using elimination 1.) -3x + 3y = 3 3x + y = 9

  18. 3.2 B: Solve the system using elimination 2.) -5x + 12y = 20 x – 2y = -6

  19. Solve the system using the substitution or elimination method. 1.) 4x + 3y = -2 2.) 3x + 3y = -15 x + 5y = -9 5x – 9y = 3

  20. Do Now: Solve the system using the elimination method. 1.) 3x – 6y = 9 -4x + 7y = -16

  21. Do Now: Solve the system using the substitution or elimination method. 2.) 12x – 3y = -9 -4x + y = 3

  22. Solve the system using any method. 2.) 3x – 7y = 10 6x – 8y = 8 1.) 2x + 5y = -5 x + 3y = 3

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