Solving Systems of Equations using Clearboards

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Solving Systems of Equations using Clearboards Note: The template for the clearboard is the last slide. © 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia (MCC9-12.A.REI.1; MCC9-12.A.REI.3; MCC9-12.A.REI.5; MCC9-12.A.REI.6; MCC9-12.A.REI.12; MCC9-12.A.REI.11)

-2x + y = 6 +2x +2x y = 2x + 6 -4x + 2(2x+6) = -6 -4x + 4x + 12 = -6 A) Solve using any method. B) Tell how many solutions the system has. C) Explain why the system has the indicated number of solutions. Ex: 1 Solve: Number of solutions: -2x + y = 6 +2x +2x y = 2x + 6 -4x + 2(2x+6) = -6 -4x + 4x + 12 = -6 12 ≠ -6 No solution Explain why: Lines are parallel

One solution (-1, -2) Lines intersect 5(-1) + y = -7 5x + y = -7 A) Solve using any method. B) Tell how many solutions the system has. C) Explain why the system has the indicated number of solutions. Ex: 2 Solve: Number of solutions: 5(-1) + y = -7 -5 + y = -7 y = -2 5x + y = -7 -5x -5x y = -5x – 7 x - 4(-5x-7) = 7 x + 20x + 28 = 7 21x + 28 = 7 -28 -28 21x = -21 x = -1 One solution (-1, -2) Explain why: Lines intersect

Infinitely many -9x + 3y = -6 +9x +9x 3y = 9x – 6 y = 3x – 2 A) Solve using any method. B) Tell how many solutions the system has. C) Explain why the system has the indicated number of solutions. Ex: 3 Solve: Number of solutions: -9x + 3y = -6 +9x +9x 3y = 9x – 6 y = 3x – 2 -3x + (3x – 2) = -2 -2 = -2 Infinitely many Explain why: Lines coincide

One solution (1.5, -1) Lines intersect 2(1.5) + 3y = 0 3 + 3y = 0 A) Solve using any method. B) Tell how many solutions the system has. C) Explain why the system has the indicated number of solutions. Ex: 4 Solve: Number of solutions: 2(1.5) + 3y = 0 3 + 3y = 0 -3 -3 3y = -3 y = -1 One solution (1.5, -1) 2x + 3y = 0 -2x -2x 3y = -2x y = -2/3x -2x + 3(-2/3x) = -6 -2x – 2x = -6 -4x = -6 x = 1.5 Explain why: Lines intersect

-5x -4y = -1 No solution +5x +5x -4y = 5x - 1 y = -5/4x + 1/4 A) Solve using any method. B) Tell how many solutions the system has. C) Explain why the system has the indicated number of solutions. Ex: 5 Solve: Number of solutions: -5x -4y = -1 +5x +5x -4y = 5x - 1 y = -5/4x + 1/4 5x + 4(-5/4x + 1/4) = 2 5x - 5x + 1 = 2 1 ≠ 2 No solution Explain why: Lines are parallel

Solve: Number of solutions: Explain why: