# SOLUTION: solve the system by addition method. if a unique solution doesn't exist, state whether the system is inconsistent or dependent. 2x-3y+z=5 x+4y-2z=-3 4x-2y+3z=6 I could really

Algebra ->  Algebra  -> Systems-of-equations -> SOLUTION: solve the system by addition method. if a unique solution doesn't exist, state whether the system is inconsistent or dependent. 2x-3y+z=5 x+4y-2z=-3 4x-2y+3z=6 I could really      Log On

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 Question 126227: solve the system by addition method. if a unique solution doesn't exist, state whether the system is inconsistent or dependent. 2x-3y+z=5 x+4y-2z=-3 4x-2y+3z=6 I could really use some. I am pulling out my hair. Please.Answer by uma(370)   (Show Source): You can put this solution on YOUR website!2x-3y+z=5 -----------(1) x+4y-2z=-3 -------------(2) 4x-2y+3z=6 --------------(3) (2) + (1)*2 gives, 5x - 2y = 7 ------------(4) (1)*3 - (3) gives, 2x - 7y = 9 -------------(5) Now the equationsa are reduced to 2 in 2 variables. (4) * 2 gives, 10x - 4y = 14 (5) * 5 gives, 10x - 35y = 45 Subtracting the above 2 equations, we get, 31 y = - 31 ==> y = -1 Plugging this in (4) gives, 5x + 2 = 7 ==> 5x = 7 - 2 ==> 5x = 5 ==> x = 1 Substituting x = 1, y = -1 in (1) , 2 + 3 + z = 5 ==> 5 + z = 5 ==> z = 5 - 5 ==> z = 0 Thus x = 1, y = -1, z = 0 Good luck!!!