9. Solve the following system of equations. x + 2y − 6 = z 3y − 2z = 7 4 + 3x = 2y − 5z A. x = 0, y = 5, z = 4 B. C. D. x = 2, y = 1, z = 2
1 answer:
X + 2y - 6 = z..........x + 2y - z = 6 3y - 2z = 7 4 + 3x = 2y - 5z.....3x - 2y + 5z = -4 x + 2y - z = 6.....multiply by -3 3x - 2y + 5z = -4 --------------------- -3x - 6y + 3z = -18 (result of multiplying by -3) 3x - 2y + 5z = -4 --------------------add -8y + 8z = - 22 -8y + 8z = -22 3y - 2z = 7 .....multiply by 4 ---------------- -8y + 8z = -22 12y - 8z = 28 (result of multiplying by 4) ----------------add 4y = 6 y = 6/4 reduces to 3/2 -8y + 8z = -22 -8(3/2) + 8z = -22 -12 + 8z = -22 8z = -22 + 12 8z = -10 z = -10/8 reduces to -5/4 x + 2y - 6 = z x + 2(3/2) - 6 = -5/4 x + 3 - 6 = -5/4 x - 3 = -5/4 x = -5/4 + 3 x = -5/4 + 12/4 x = 7/4 solution is (7/4, 3/2, -5/4).....x = 7/4, y = 3/2, and z = -5/4
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