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Solving System of Linear Equations

Solving System of Linear Equations. Elimination Method. y - 2x = -3. y - x = -1. Warm-up: solve the linear system by Elimination. (2,1). (5). -22. -22. -2. -2. (. - 30. ). - 30. (5). Multiplying one equation. -2x - 5y = 22 10x + 3y = 22. -2x - 5y = 22. -2x - 5 y = 22.

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Solving System of Linear Equations

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  1. Solving System of Linear Equations • Elimination Method

  2. y - 2x = -3 y - x = -1 Warm-up: solve the linear system by Elimination (2,1)

  3. (5) -22 -22 -2 -2 ( - 30 ) - 30 (5) Multiplying one equation -2x - 5y = 22 10x + 3y = 22 -2x - 5y = 22 -2x - 5y = 22 -2x - 5(-6) = 22 -2x + 30 = 22 -10x - 25y = 110 10x + 3y = 22 -2x = -8 0 - 22y = 132 x = 4 - 22y = 132 y = -6 (4, -6)

  4. (2) 4 8 8 4 ( - 14 ) - 14 (2) Your turn! 4x + 2y = -10 -2x + 3y = 33 4x + 2y = -10 4x + 2y = -10 4x + 2(7) = -10 4x + 14 = -10 4x + 2y = -10 -4x + 6y = 66 4x = -24 0 + 8y = 56 x = -6 8y = 56 y = 7 (-6, 7)

  5. 20 = 20 4 4 4x + 10y = 70 4x + 10y = 70 Your turn… again! -4x + 10y = -50 2x - 5y = 25 -2(2x - 5y = 25) 4x + 10y = 70 4x + 10y = 70 -4x + 10y = -50 4x + 10(1) = 70 4x + 10 = 70 20y = 20 -10 = -10 4x = 20 y = 1 x = 5 Answer: (5,1)

  6. Practice! Hint: multiply the first equation by 4 2x - y = 9 3x + 4y = -14 Answer: ( 2, -5 )

  7. (-3) (5) 3 4 3 4 ( ( - 25 ) ) - 25 (-3) (5) Multiplying two equations 3x + 5y = 10 5x + 7y = 10 3x + 5y = 10 3x + 5y = 10 3x + 5(5) = 10 3x + 25 = 10 15x + 25y = 50 -15x - 21y = -30 3x = -15 0 + 4y = 20 x = -5 4y = 20 y = 5 (5, -5)

  8. (-2) (3) + 21 -13 -13 10 2 ( ( ) ) +21 (-2) (3) Your Turn! 2x - 3y = -11 3x + 2y = 29 2x - 3y = -11 2x - 3y = -11 2x - 3(7) = -11 2x - 21 = -11 6x - 9y = -33 -6x -4y = -58 2x = 10 0 -13y = -91 x = 5 -13y = -91 y = 7 (7, 5)

  9. y = ½x + 1 y = -⅔x 2.) y = x + 4 y = 3x 4x - 3y = 11 3x - 5y = -11 1.) y = -½x + 1 y = -5x -1 3.) 2x + y = 8 y = x - 7 x + 2y = 7 3x - 2y = 1 y = 3x - 6 -3x + y = -6 8x - 9y = 19 4x + y = -7 y = 2x - 3 y = -3x + 2 1.) 2.) 3.) 2.) 3.) 1.) Summary: On Solving Linear Systems(Graphing, Substitution, Elimination Methods) Graphing: Substitution Elimination

  10. Classwork 1.) 2.) 8x + 11y = 20 5x - 11y = -59 2x - 3y = 61 2x + y = -7 3.) 4.) 2x - 3y = 5 x + 2y = -1 20x + 3y = 20 -20x + 5y = 60

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