Question

Solve the system by substitution, show all steps.
-x-y-z=-8
-4+4y+5z=7
2x+2z=4

Answer 1

In Point Form: (x,y,z)= (3,6,-1)

In Equation Form: x=3, y=6, z=-1

Explanation:

1) Solve for x

2x+2z=4 (Subtract 2z from both sides)

-2z -2z

2x= 4-2z (Divide 2 from both sides)

/2 /2

x=2-z

2) Substitute 2-z for x in

-x-y-z=-8

-(2-z)-y-z=-8

-2+z-y-z=-8 (Combine Like Terms)

-2-y=-8 (Add 2 to both sides)

+2 +2

-y=-6 (Divide -1 from both sides)

/-1 /-1

y=6

3) Substitute 2-z for x & 6 for y in

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

-4(2-z)+4(6)+5z=7 (Get rid of parentheses)

-8+4z+24+5z=7 (Combine Like Terms)

9z+16=7 (Subtract 16 from both sides)

-16 -16

9z+=-9 (Divide 9 from both sides)

/9 /9

z=-1

4) Now find x by substituting -1 for z in

x=2-z

x=2-(-1)

x=2+1

x=3

Therefore the answer is:

In Point Form: (x,y,z)= (3,6,-1)

In Equation Form: x=3, y=6, z=-1

Answer 2

from the third equation 2z=-2x+4
z=-x+2
plug into the second equation -4+4y+5(-x+2)=7
-4+4y-5x+10=7
4y-5x=1
y=5/4x+1/4
plug both of these into the first equation x+y+z=8
x+5/4x+1/4+(-x+2)=8
5/4x+2.25=8
5/4x=5.75
x=4.6
now plug back into the substitution equations.
z=-x+2= -4.6+2= -2.6
y=5/4x+1/4=5.75+1/4=6

the answer is (4.6, 6, -2.6)