Question

X+y+3z=-16
x+y+7z=-32
x-8y-6z=11

Answer 1

If we subtract first equation - second we get:-

-4z = 16 so z = -4

Plugging in z = -4 into 2nd and third equations we get

x + y - 28 = -32

x + y = -4 (1)

x - 8y = -13 (2)

Subtract (1) - (2)

9y = 9

so y = 1

Plug y=1 and z = -4 into (1):-

x + 1 = -4

x = -5

Answer is x = -5, y = 1 and z = -4.

Answer 2

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

`(-4z)/(-4) =(16)/(-4)` 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