Mathematics
AlejandroIkeard
4

Which ordered triple is a solution of this system? 2x+y-z=7 -x-2y+4z=-15 x+2y-5z=17 A.(-2,6,-5) B.(1,3,-2) C.(2,5,2) D.(3,1,0)

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(1) Answers
FlorineCrayton

The problem is an example of systems of linear equation with 3 variables. In order for us to get  the solutions, we need to use Elimination. (1) Add the two equations to get z -x-2y+4z=-15 x+2y-5z=17 -------------------- -z = 2 z = -2 Then lets multiply 2x+y-z=7  by 2 --> 4x + 2y - 2z = 14 Then add it -x-2y+4z=-15 4x + 2y - 2z = 14 -x-2y+4z=-15 ----------------- -3x + 2z = -1 Substitute z to that equation -3x + 2(-2) = -1 -3x - 4 = -1 -3x = 3 x = 1 Then, using this equation 2x+y-z=7, substitute z and x 2(1) + y -(-2) = 7 2 + y +2 = 7 y = 7 -4 y = 3 So, the final answer is B.(1,3,-2)

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