You can put this solution on YOUR website! x+(1/3y)+z=13
(1/2x)-y+(1/3z)=-2
x+(1/2y)-(1/3z)=2
Take LCM and simplify the equations to eliminate the denominators
3 x + 1 y + 3 z = 39 -------------- 1
3 x + -6 y 2 z = -12 -------------- 2
6 x + 3 y + -2 z = 12 -------------- 3
consider equation 1 &2 Eliminate y
Multiply 1 by 6 -5
Multiply 2 by 1 4
we get
18 x + 6 y + 18 z = 234
3 x + -6 y + 2 z = -12
Add the two
21 x + 0 y + 20 z = 222 ------------- 4
consider equation 2 & 3 Eliminate y
Multiply 2 by 1
Multiply 3 by 2
we get
3 x + -6 y + 2 z = -12
12 x + 6 y + -4 z = 24
Add the two
15 x + 0 y + -2 z = 12 -------------5 5
Consider (4) & (5) Eliminate x
Multiply 4 by -15
Multiply (5) by 21
we get
-315 x + -300 z = -3330
315 x + -42 z = 252
Add the two
0 x + -342 z = -3078
/ -342
z = 9
15 x + -2 z= 12
15 x + -18 = 12
x = 2
Plug x & z in eq (1)
3 x + 1 y + 3 z = 39 -------------- 1
6 + 1 y + 27 = 39
1 y = 6
y = 6
x= 2 y= 6 z= 9
