Question

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

Answer 1

since we have an equation that only has to variables, we will need to get another equation to those two variables

Answer 2

so we need to replace y, and the easiest way to find y= would be in the first equation

Answer 3

so what does y=?

Answer 4

I don't know...

Answer 5

from the first one ...
-x-y-z=-8
-( x + y + z) = -8
x + y + z = 8 ---- (1)

from the last one
2x+2z=4
2 ( x + z ) = 4
x + z = 2 ---- (2)

now substitute x + z = 2 in ( 1)
y + 2 = 8
y = 6

from (2)
x + z = 2
z = 2 -x

now take ..
-4x+4y+5z=7
-4( x - y) + 5z = 7

substitute z = 2 -x here..
-4( x - y) + 5z = 7
-4( x - y) + 5(2 -x)= 7
-4x+4y + 10 - 5x = 7
-9x + 4y = 7 -10 = -3

substitute y = 6
-9x + 24 = -3
9x = 27
x = 3
from (2)
z = 2 -x
= 2 - 3
= -1

hope this will help ya!!

Answer 6

thats okay
-x-y-z=-8 so we want y alone so add x and y to both sides
-y=-3+x+z then multiply by -1 go make y positive
y=3-x-z

Answer 7

so this is what we will substitute for y in the 2nd equation

Answer 8

woah sorry not 3 8

Answer 9

-4x+4y+5z=7 so lets input y
-4x+4(8-x-z)+5z=7 distribute
-4x+32-4x-4z+5z=7 then simplify
-8x+z+32=7 subtract 32 from both sides
-8x+z=-25

Answer 10

so sorry

Answer 11

anyway
-8x+z=-25
2x+2z=4 divide by -2 to remove z
-8x+z=-25
-x-z=-2 add the two equations
-9x=-27
x=3

Answer 12

lets reinput x into 2x+2z=4
2(3)+2z=4 simplify
2z+6=4 subtract -6 from both sides
2z=-2 divide by 2
z=-1

Answer 13

so now we input x and z into the first equation
-x-y-z=-8
-3-y-(-1)=-8 simplify
-3-y+1=-8
-y-2=-8
-y=-6
y=6

Answer 14

so x=3 y=6 z=-1

Answer 15

Thank you!! Can you help me with another one?

Answer 16

ok

Answer 17

Solve the system by elimination
-2x+2y+3z=0
-2x-y+z=-3
2x+2z=4

Answer 18

@insanitycat

Answer 19

so lets get y from the second equation
-2x-y+z=-3 so add 2x to both sides and subtract z
-y=-3+2x-z now multiply by -1 to get y positive
y=3-2x+z

Answer 20

not lets substitute y into the first equation
-2x+2y+3z=0
-2x+2(3-2x+z)+3z=0 distribute
-2x+6-4x+2z+3z simplifly
-6x+5z+6=0 subtract 6 from both sides
-6x+5z=-6

Answer 21

so now we have
2x+2z=4 lets multiply this equation by 3
-6x+5z=-6

6x+6z=12
-6x+5z=-6 add the two
11z=6
z=6/11

Answer 22

lets input z into 2x+2z=4
2x+2(6/11)=4
2x+12/11=4 or 44/11 subtract 12/11 from both sides
2x=32/11 multiply by 1/2
x=16/11

Answer 23

now lets input both into the 2nd equation
-2x-y+z=-3
-2(16/11)-y+6/11=-3 simplify
-32/11-y+6/11=-3
-y-26/11=-3 or -33/11 add 26/11 to both sides
-y=-7/11 multiply by -1
y=7/11

Answer 24

so x=16/11 y=7/11 and z=6/11

Answer 25

Okay so what I have is
1. Get y from second equation -2x-y+z=-3
2. Add 2x to both sides and subtract z -y=3-2x+z
3. Multiply by -1 to get y positive y=3-2x+z
4. Substitute y into first equation -2x+2y+3z=0 becomes -2x+2(3-2x+z)+3z=0
5. Distribute -2x+6-4x+2z+3z
6. Simplify -6x+5z+6=0
7. Subtract 6 from both sides -6x+5z=-6

Answer 26

yes

Answer 27

8. Multiply the equation 2x+2z=4 by 3 -6x+5z=6

Answer 28

I actually messed up the equation. It's supposed to be Solve the system by elimination
-2x+2y+3z=0
-2x-y+z=-3
2x+3y+3z=5

Answer 29

so lets elimate to get equations with two variables
2x+3y+3z=5
-2x+2y+3z=0
5y+6z=5
and
2x+3y+3z=5
-2x-y+z=-3
2y+5z=-2

Answer 30

sorry 2y+4z=2
5y+6z=5 multiply this by 2
2y+4z=2 multiply this by -3
10y+12z=10
-6y-12z=-6
4y=4
y=1

Answer 31

so substitute y into one of the equations ill use 2y+4z=2
2(1)+4z=2
4z+2=2
4z=0
z=0

Answer 32

so lets subsitute y and z now
2x+3y+3z=5
2x+3(1)+3(0)=5
2x+3=5
2x=2
x=1

Answer 33

so x=1 y=1 and z=0