Question

25 POINTS!!!! PLEASE EXPLAIN TO ME STEP BY STEP!

Solve the system by substitution.

-x-y-z=-8
-4x+4y+5z=7
2x+2z=4

I am very confused about this. Can someone please explain how to do this?

Answer 1

-x-y-z=-8
-x-y-z=-8

Let's solve for x.−x−y−z=−8
Step 1: Add y to both sides.−x−y−z+y=−8+y−x−z=y−8
Step 2: Add z to both sides.−x−z+z=y−8+z−x=y+z−8
Step 3: Divide both sides by -1.−x−1=y+z−8−1x=−y−z+8
Answer: x=−y−z+8

Answer 2

easy peassy
so basically what you would try to do is eliminate one type of variable from 2 different equations
look, we have
2x+2z=4
that already has y eliminated
so we just need to eliminate y from another equation

so

we can eliminate the y from the 2nd equation
multiply the first equation by 4 and add to 2nd equation

-4x-4y-4z=-32
-4x+4y+5z=7 +
-8x-0y+1z=-25

-8x+z=-25


we have
-8x+z=-25 and
2x+2z=4

we can elminate the z's
multiply first (top) equation by -2 and add to bottom equaton
16x-2z=50
2x+2z=4 +
18x=54

18x=54
divide both sides by 18
x=3

sub back
2x+2z=4
2(3)+2z=4
6+2z=4
minus 6 both sides
2z=-2
divide 2
z=-1

sub back

-x-y-z=-8
-3-y-(-1)=-8
-3-y+1=-8
-2-y=-8
add 2 to both sides
-y=-6
times -1
y=6


x=3
y=6
z=-1
(x,y,z)
(3,6,-1)