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ALGEBRA II HONORS @

ALGEBRA II HONORS @. SECOND ORDER DETERMINANTS (Cramer’s Rule). Solve using elimination : 9x – 7y = 5 10x + 3y = -16. = (5 • 3) – (-16 • -7) = 15 - 112 = -97. 2) Now, solve the same system using a slightly different technique. matrix. = (9 • -16 ) – (10 • 5) = -144 - 50 = -194.

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ALGEBRA II HONORS @

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  1. ALGEBRA II HONORS @ SECOND ORDER DETERMINANTS (Cramer’s Rule)

  2. Solve using elimination : • 9x – 7y = 5 • 10x + 3y = -16 = (5 • 3) – (-16 • -7) = 15 - 112 = -97 2) Now, solve the same system using a slightly different technique. matrix = (9 • -16 ) – (10 • 5) = -144 - 50 = -194 = (9 • 3) – (10 • -7) = 27 + 70 = 97 This technique is called Cramer’s Rule. D means determinant, which is a value for a matrix. Therefore, the answer is (-1, -2)

  3. Solve using Cramer’s Rule. 3) 3x + 4y = 8 2x – 2y = 7 4) 3x + 7y = 11 8x + 5y = 13

  4. 5) 2x – 6y = 7 4x – 12y = 10 6) 3x + 2y = -8 -6x – 4y = 16 7) -7x + 14y = 7 4x - y = -11 Groups 1-2 do #5 Groups 3-4 do #6 Groups 5-6 do #7

  5. PROOF OF CRAMER’S RULE ax + by = c dx + ey = f Now, find y using Cramer’s Rule. Solve for y. d • (ax + by) = c • d -a • (dx + ey) = f • -a D = ae - bd adx + bdy = cd -adx – aey = -af bdy – aey = cd - af y(bd – ae) = cd - af The proof for x is similar.

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