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Use the elimination method to solve the following system of equations. 4x – 2y – z = –5 x – 3y + 2z = 3 3x + y – 2z = –5

Mathematics
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4x - 2y - z = -5 x - 3y + 2z = 3 -->(-4) --------------- 4x - 2y - z = - 5 (result of multiplying by -4) -4x + 12y - 8z = - 12 ----------------add first two equations 10y - 9z = - 17 x - 3y + 2z = 3 -->(-3) 3x + y - 2z = - 5 --------------- -3x + 9y - 6z = - 9 (result of multiplying by -3) 3x + y - 2z = - 5 ----------------add last two equations 10y - 8z = - 14 now add the answers of both sets of equations... 10y - 9z = - 17 -->(-1) 10y - 8z = - 14 -------------- -10y + 9z = 17 (result of multiplying by -1) 10y - 8z = - 14 ---------------add z = 3 Now sub 3 in for z in either of the above equations... 10y - 8z = - 14 10y - 8(3) = - 14 10y - 24 = - 14 10y = - 14 + 24 10y = 10 y = 1 now sub 1 in for y and 3 in for z in any of the first 3 equations 4x - 2y - z = - 5 4x - 2(1) - 3 = - 5 4x - 2 - 3 = - 5 4x = - 5 + 5 4x = 0 x = 0 Now sub all 3 known variables into any of the first 3 equations to check your answers... x - 3y + 2z = 3 0 - 3(1) + 2(3) = 3 -3 + 6 = 3 3 = 3 (correct) ANSWER : (0,1,3) <--- x = 0, y = 1, z = 3 :)
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