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Solving Systems by Elimination & Matrices

Solving Systems by Elimination & Matrices. EQ: For what type of problems would elimination and matrices be the best method to use?. Matrices & Elimination. Works only with linear equations (no x 2 , x 3 , |x|, √x) All variables must be moved to one side. Elimination.

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Solving Systems by Elimination & Matrices

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  1. Solving Systems by Elimination & Matrices EQ: For what type of problems would elimination and matrices be the best method to use?

  2. Matrices & Elimination • Works only with linear equations (no x2, x3, |x|, √x) • All variables must be moved to one side

  3. Elimination • Step 1: Line up equations • Step 2: Multiply one or both equations so that you have a pair that will cancel • Step 3: Add equations together • Step 4: Solve for the variable • Step 5: Go back and find the other variable

  4. Ex 1) Solve the system using elimination 2x – 3y = 12 4x + 3y = 6 + 6x = 18

  5. Ex 2) Solve the system using elimination 3x – 4y = 18 3x + 9y = -7 -3x - 9y = 7 -13y = 15

  6. Ex 3) Solve the system using elimination 3x – 2y = 8 5x + 4y=28 6x – 4y = 16 5x + 4y= 28 11x = 44

  7. Matrix • Row by Column ROW COLUMN

  8. Reduced Row Echelen Form • A matrix with only leading 1’s and 0’s everywhere else

  9. Solving using “ rref ” ax + by = c dx + ey = f x = r y = s

  10. How to find RREF using Calculator: 2nd, MATRIX (x -1), EDIT, [A] Make a 2 by 3 or 3 by 4 matrix Enter coefficients 2nd, Quit (Mode) 2nd, x -1 → MATH, rref( 2nd, x -1 , #1 [A] Press Enter

  11. Ex 4. Solve the system using matrices

  12. Ex 5. Solve the system using matrices

  13. Ex 6. Solve by your method of choice

  14. Solve by Matrices or Elimination 1. 5x + 2y = 8 2. 2x + y = 2 x – y = 10 -2x + 2y = 10 3. y = -2x – 4 4. 5x + 3y = -6 { { (-1, 4) (4, -6) { (0, 2) (-6, 8)

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