Question

Solve the system by substitution -x-y-z=-8 -4x+4y+5z=7 2x+2z=4 show the work

Answer 1

ANSWER

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

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