Question

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)

Answer 1

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)