Let
-x - y - z = -8 ........ (1a)
-4x + 4y +5z = 7 ..... (2a)
2x + 2x = 4 .......... (3a)
since (3a) a is an equation solely in x make x the subject of the equation
2 ( x + x) = 4
divide both sides by 2
(x + x) = 2
2x = 2
x = 1 ....... (3b)
substitute x in (3b) for x in (1a)
-(1) - y - z = -8
make y the subject of the equation
-y - z = -8 + 1
-y = -7 + z
y = 7 - z ..... (1b)
substitute y in (1b) for y in (2a) as well as the value of x ( x= 1)
-4(1)+ 4( 7 - z ) +5z = 7
- 4 + 28 - 4z + 5z = 7
-24 + z = 7
z = 7 + 24
z = 31
By using (1a) solve for y
-(1) - y - (31)= -8
-1 - y - 31 = -8
y = -1 - 31 + 8
y = -24
∴ the solutions of the system are x = 1 ; y = -24 ; z = 31
