Question

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

Answer 1

first isolate x in the third equation so
2x + 2z = 4 => 2x = -2z + 4 => x= -z + 2
then you can plug x into the first equation and reduce so
-x -y -z = -8 => -(-z+2)-y-z=-8 => z-2-y-z=-8 => y=6
substitute x and y into the second equation so
-4x+4y+5z=7 => -4(-z+2)+4(6)+5z=7 => 4z-8+24+5z=7
=> 9z=-9 => z=-1
then you can substitute z into the third equation to find x
2x+2z=4 => 2x+2(-1)=4 => 2x-2=4 => 2x=6 => x=3

so x=3, y=6, and z=-1

Answer 2

Thanks!

Answer 3

Just to make things easier, I multiplied the first equation by -1
A) x + y + z = 8
B) -4x + 4y + 5z = 7
C) 2x + 2z = 4
equation C can be changed to
x = 2 -z
Substituting this into equation A
2 - z + y + z = 8 equals
y = 6 we can substitute this into equation 1 and 2
A) x + 6 + z = 8
B) -4x + 24 + 5z = 7 OR
B) -4x +5z =-17

A) x + z = 2
B) -4x +5z = -17

A) x = 2 -z then substituting this into B)

B) -4* (2-z) + 5z = -17
-8 +4z + 5z = -17
9z = -9
z=-1

Substituting z = -1 into equation C

2x + 2z = 4
2x -2 = 4
x = 3