# Solving Three Variable Linear Equation:6x-5z=17 5x-y+3z=-1 2x+y=-41Solving 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*

The system of equations 6x-5z=17, 5x-y+3z=-1 and 2x+y=-41 has to be solved.

6x-5z=17

=> z = (6x - 17)/5

2x+y=-41

=> y = -41 - 2x

Substitute for z and y in 5x-y+3z=-1

5x + 41 + 2x + 3*(6x - 17)/5 = -1

25x + 205 + 10x + 3*(6x - 17) = -5

25x + 205 + 10x + 18x - 51 = -5

53x = -159

x = -159/53

x = -3

y = -41 - 2x = -41 + 6 = -35

z = (6x - 17)/5 = -35/5 = -7

The solution of the system of equations is x = -3, y = -35 and z = -7