Solving Linear Systems

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Using the graphing, substitution, and addition methods to solve linear systems

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Solving Linear Systems

  1. 1. Review problems: Solving by using Graphing Substitution Addition Word problem Linear Systems
  2. 2. y = 2x + 1 x + 2y = 7 1. Solve by graphing Now use the table or calculate:intersect option Solve both equations for y: Solution (1, 3)
  3. 3. x = y - 2 x + y = 18 2. Solve by using the Substitution Method in place of x, substitute (y - 2) NOW SOLVE FOR Y (y - 2) + y = 18 2y - 2 = 18 +2 +2 2y = 20 2 2 y = 10 NOW THAT YOU KNOW THAT y = 10, SUBSTITUTE INTO ONE OF THE ORIGINAL EQUATIONS TO FIND x x = y - 2 x = (10) - 2 x = 8 SOLUTION: (8, 10)
  4. 4. 3a - b = 3 a + 3b = 11 3. Solve by using the Addition Method 3a - b = 3 a + 3b = 11 Multiply by 3 to get (-3b) in the first equation which when added together to (+3b) in the second equation will then cancel out. This will allow you to solve for a. 9a - 3b = 9 a + 3b = 11 NOW THAT YOU KNOW THAT a = 2, SUBSTITUTE INTO ONE OF THE ORIGINAL EQUATIONS TO FIND b a + 3b = 11 (2) + 3b = 11 2 + 3b = 11 -2 -2 3b = 9 3 3 b = 3 SOLUTION: a = 2, b = 3 3( ) 10a = 20 10 10 a = 2 +
  5. 5. <ul><li>Set up a system of equations to solve the equation algebraically. </li></ul>On one day, 4 gardeners and four helpers earned $360. On another day, working the same number of hours and at the same rate of pay, five gardeners and six helpers earned $480. How much does a gardener and how much does a helper earn each day? g: gardeners h: helpers 4g + 4h = 360 5g + 6h = 480
  6. 6. NOW THAT YOU KNOW THAT h = 30, SUBSTITUTE INTO ONE OF THE ORIGINAL EQUATIONS TO FIND g 4g + 4h = 360 4g + 4(30) = 360 4g + 120 = 360 - 120 -120 4g = 240 4 4 g = 60 SOLUTION: Gardeners make $60 an hour, Helpers make $30 an hour 4g + 4h = 360 5g + 6h = 480 -5( ) -20g - 20h = -1800 4h = 120 4 4 h = 30 20g + 24h = 1920 4( )
  7. 7. 5. What is a linear system? A set of two or more linear equations

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