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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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**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 x2, x3, |x|, √x) • All variables must be moved to one side**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**Ex 1) Solve the system using elimination**2x – 3y = 12 4x + 3y = 6 + 6x = 18**Ex 2) Solve the system using elimination**3x – 4y = 18 3x + 9y = -7 -3x - 9y = 7 -13y = 15**Ex 3) Solve the system using elimination**3x – 2y = 8 5x + 4y=28 6x – 4y = 16 5x + 4y= 28 11x = 44**Matrix**• Row by Column ROW COLUMN**Reduced Row Echelen Form**• A matrix with only leading 1’s and 0’s everywhere else**Solving using “ rref ”**ax + by = c dx + ey = f x = r y = s**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**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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