Solving Systems of Equations by Elimination Part 2

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Presentation transcript:

Solving Systems of Equations by Elimination Part 2

Solve the System of Equations These need to have the same coefficient with opposite signs ( ) 2x + y = 20 10x + 5y = 100 • (5) = 6x - 5y = 12 6x -5 y = 12 16x + 0y = 112 16x = 112 6x - 5y = 12 x = 7 6(7) - 5y = 12 42 - 5y = 12 -5y = -30 y = 6 Solution (7, 6)

  Check 6x - 5y = 12 2x + y = 20 6(7) - 5(6) = 12 2(7) + 6 = 20 Solution (7, 6) 6x - 5y = 12 2x + y = 20 6(7) - 5(6) = 12 2(7) + 6 = 20 42 - 30 = 12 14 + 6 = 20 12 = 12  20 = 20 

Solve the System of Equations These need to have the same coefficient with opposite signs ( ) -5x + y = -3 -40x + 8y = -24 • (8) = 3x - 8y = 24 3x - 8 y = 24 -37x + 0y = 0 -37x = 0 3x - 8y = 24 x = 0 3(0) - 8y = 24 0 - 8y = 24 -8y = 24 y = -3 Solution (0, -3)

  Check 3x - 8y = 24 -5x + y = -3 3(0) - 8(-3) = 24 -5(0) + -3 = -3 Solution (0, -3) 3x - 8y = 24 -5x + y = -3 3(0) - 8(-3) = 24 -5(0) + -3 = -3 0 - -24 = 24 0 + -3 = -3 24 = 24  -3 = -3 

Solve the System of Equations These need to have the same coefficient with opposite signs ( ) -7x - 8y = 9 -63x - 72y = 81 • (9) = -4x + 9y = -22 ( ) -32x +72y = -176 •(8)= -95x + 0y = -95 -95x = -95 -4x + 9y = -22 x = 1 -4(1) + 9y = -22 -4 + 9y = -22 9y = -18 y = -2 Solution (1, -2)

  Check -4x + 9y = -22 -7x - 8y = 9 -4(1) + 9(-2) = -22 Solution (1, -2) -4x + 9y = -22 -7x - 8y = 9 -4(1) + 9(-2) = -22 -7(1) - 8(-2) = 9 -4 + -18 = -22 -7 + 16 = 9 -22 = -22  9 = 9 

Solve the System of Equations These need to have the same coefficient with opposite signs ( ) 3x - 2y = 2 -15x + 10y = -10 • (-5) = ( ) 10x - 10y = 20 5x - 5y = 10 • (2) = -5x + 0y = 10 -5x = 10 3x - 2y = 2 x = -2 3(-2) - 2y = 2 -6 - 2y = 2 -2y = 8 y = -4 Solution (-2,-4)

  Check 5x - 5y = 10 3x - 2y = 2 5(-2) - 5(-4) = 10 Solution (-2, -4) 5x - 5y = 10 3x - 2y = 2 5(-2) - 5(-4) = 10 3(-2) - 2(-4) = 2 -10 + 20 = 10 -6 + 8 = 2 10 = 10  2 = 2 