Question

Solve the system by substitution

-x-y-z=-8
-4x+4y+5z=7
2x+2z=4

show the work

Answer 1

`x=3,y=6,z=-1`

Step-by-step explanation

We the have the equations,

`-x-y-z=-8`

Multiplying through by negative one gives,

`x+y+z=8---(1)`

Also

`-4x+4y+5z=7---(2)`

and

`2x+2z=4`

Dividing through by 2 gives

`x+z=2`

Making z the subject gives,

`z=2-x---(3)`

Now we substitute equation (3) into equation (1) and (2)

Equation (3) in to equation (1) gives,

`x+y+2-x=8`

This implies that;

`y=8-2`

`y=6`

We now put equation (3) in (2) to get,

`-4x+4y+5(2-x)=7`

This implies that

`-4x+4y+10-5x=7`

`-9x+4y=7-10`

`-9x+4y=-3`

But

`y=6`

So,

`-9x+4(6)=-3`

`-9x+24=-3`

`-9x=-3-24`

`-9x=-27`

Dividing through by negative 9 gives

`x=3`

and

`z=2-3`

`z=-1`

Therefore
`x=3,y=6,z=-1`