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System Solving Methods in Algebra II

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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