Solve the system by substitution

-x-y-z=-8

-4x+4y+5z=7

2x+2x=4

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