Solving Three Variable Linear Equation:6x-5z=17 5x-y+3z=-1 2x+y=-41 Solving Three Variable Linear Equation... HELP.... seriously confusing. it will give you a headache.

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`6x-5z=17` -----(1)


`5x-y+3z=-1` ----(2)


`2x+y=-41` ----(3)

 

`(1)+(3)`

`8x+y-5z = -24` -----(4)

 

`(2)+(4)` ---> y will cancel out.

`13x-2z = -25 ` ----(5)

 

`(1)*2-(5)*5` ----> z will cancel out

`12x-65x = 17*2+25*5`

      `-53x = 159`

            `x = -3`

 

From (5)

`z = (-25-13*(-3))/(-2) = -7`

 

From (3)

 `y = -41-2*(-3) = -35`

 

So the answers are;

x = 2

y = -35

z = -7

Approved by eNotes Editorial Team

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