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System Solving Methods in Algebra II

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Learn to solve linear systems graphically and algebraically in Algebra II. Practice problems and tests included for Substitution and Elimination methods. Application questions are also provided.

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System Solving Methods in Algebra II

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  1. Algebra II 3.1: Solve Linear Systems by Graphing HW: p.156 (4, 8, 10, 12), review old graphing: absolute value, quadratics, etc. Test: Next week Thursday

  2. 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?

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

  4. Find the solution to the system graphically. 2.) y = 2 x = -4 3.) 2x + y = 4 -4x - 2y = -2 4.) y = -1 3x + y = 5

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

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

  7. Algebra II 3.2: Solve Linear Systems Algebraically HW: 164 (28-38 even) Test: Thursday, 4/2

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

  9. Solve the system using the substitution method. 2x + 5y = -5 x + 3y = 3

  10. Solve the system using the elimination method. 3x – 7y = 10 6x – 8y = 8

  11. Solve the system using the substitution or elimination method. 1.) 4x + 3y = -2 2.) 3x + 3y = -15 x + 5y = -9 5x – 9y = 3 3.) 3x – 6y = 9 4.) 12x – 3y = -9 -4x + 7y = -16 -4x + y = 3

  12. Solve the system using the substitution or elimination method. 3.) 3x – 6y = 9 4.) 12x – 3y = -9 -4x + 7y = -16 -4x + y = 3

  13. 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?

  14. 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?

  15. 3.4: Solve the system. 4x + 2y + 3z = 1 2x – 3y + 5z = -14 6x – y + 4z = -1

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