x+y+3z=-16 ... (1)
x+y+7z=-32 ...(2)
x-8y-6z=11 ... (3)
Let's subtract equation (1) and (2) so that we can eliminate x and y. So,
x+y+3z=-16
x+y+7z=-32
____________________
(x-x)+(y-y)+(3z-7z)=(-16)-(-32)
0+0-4z=-16+32
-4z= +16
Dividing each sides by -4.
z=-4
Now plug in z=-4 in equation (2) and (3). So, by plug in -4 for z in equation (2) we will get
x+y+7(-4)=-32
x+y-28=-32
x+y=-32+28
x+y=-4 ....(equation (4)
Now let's plug into equation (3). So,
x-8y-6(-4)=11
x-8y+24=11
x-8y=11-24
x-8y=-13 ......... equation(5)
Now we have two equations (4) and (5) with two variables x and y which we can solve now.
We can eliminate y from equation (4) and (5) by making equal and opposite coefficient of y's. So, multiply equation (4) by 8.
(x+y=-4)x8
8x+8y=-32....... (6)
Now after adding equation (5) and (6) wewill get,
9x=-45
9x/9=-45/9
x=-5
Now we can plug in x=-5 and z=-4 in any equation to get the value of y. So, let's plug in to equation (1).
-5+y+3(-4)=-16
-5+y-12=-16
y-17=-16
y=17-16
y=1
So, x=-5, y=1 and z=-4