Solving System of Linear Equations

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Presentation transcript:

Solving System of Linear Equations Elimination Method

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

Multiplying one equation (5) ( ) -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 - 30 -2x = -8 0 - 22y = 132 -2 x = 4 - 22y = 132 -22 y = -6 (4, -6)

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

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

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

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

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

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

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