Question

can some one help me please with solving by substitution

Answer 1

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

Answer 2

Take the third equation, and solve for x.

Answer 3

how do i do that i have no clue how to go this

Answer 4

Start with the third equation.
Subtract 2z from both sides.
Then divide both sides by 2.

Answer 5

wait so what would that look like

Answer 6

\(2x + 2z = 4\)

\(2x = -2z + 4\)

\(x = -z + 2\)

Answer 7

Now that equation 3 is solved for x, substitute x from equation 3 into both equations 1 and 2.
Then you have a system of 2 equations in two variables which can be solved easily.

Answer 8

im not sure how to do that

Answer 9

@song_of_the_sole do you see how @mathstudent55 got `x = -z+2` ?

Answer 10

kinda but Im still unsure how to do the rest can u help walk me through it

Answer 11

you would replace 'x' in -x-y-z=-8 with -z+2

what do you get when you do so?

Answer 12

thats the part that is confusing me is the plugging it in that im not confident in

Answer 13

\[\Large -x-y-z = -8\]
\[\Large -1*x-y-z = -8\]
\[\Large -1*(x)-y-z = -8\]
\[\Large -1*({\color{red}{x}})-y-z = -8\]
\[\Large -1*({\color{red}{-z+2}})-y-z = -8\]
Do you see how I did those steps?

Answer 14

yea

Answer 15

Do you know how to simplify that?

Answer 16

not really

Answer 17

Distribute the -1 for `-1(-z+2)` to get what?

Answer 18

-1z-2

Answer 19

-1 times -z = ???

Answer 20

-z

Answer 21

negative times negative = ????

Answer 22

oh sorry positive z

Answer 23

So this means
\[\Large -1*(-z+2)-y-z = -8\]
turns into
\[\Large z-2-y-z = -8\]

Answer 24

are there any like terms on the left side?

Answer 25

the z

Answer 26

yep, so what do the z terms combine to?

Answer 27

1z-2-y=-8

Answer 28

we have a 'z' and then a '-z'

Answer 29

z-z = ???

Answer 30

none

Answer 31

yep so the 'z' terms go away

Answer 32

we have this left over: `-2-y = -8`

Answer 33

at this point, you probably see how to solve for y?

Answer 34

add 2

Answer 35

yep add 2 to both sides. Giving you what?

Answer 36

-6

Answer 37

-y = -6

so, y = ???

Answer 38

6

Answer 39

yep

Answer 40

now that we know y = 6, we can replace y in the first equation -x-y-z=-8 to get...

-x-y-z=-8
-x-6-z=-8
-x-6-z+6=-8+6
-x-z = -2

do you agree with those steps?

Answer 41

yes

Answer 42

So we have `-x-z = -2` and we know that `x = -z+2` (based on what @mathstudent55 wrote). Do you see how to use substitution?

Answer 43

kinda

Answer 44

but what about z we found x and y what about z

Answer 45

\[\Large -x-z = -2\]
\[\Large -1*x-z = -2\]
\[\Large -1*(x)-z = -2\]
\[\Large -1*({\color{red}{x}})-z = -2\]
\[\Large -1*({\color{red}{-z+2}})-z = -2\]

Answer 46

ok...

Answer 47

sorry I picked on the wrong equation

Answer 48

\[\Large -4x+4y+5z=7\]
\[\Large -4*(x)+4*(y)+5z=7\]
\[\Large -4*({\color{red}{x}})+4*({\color{blue}{y}})+5z=7\]
\[\Large -4*({\color{red}{-z+2}})+4*({\color{blue}{6}})+5z=7\]
\[\Large -4(-z)-4(2)+4(6)+5z=7\]
\[\Large 4z-8+24+5z=7\]
solve for z and tell me what you get

Answer 49

9z+16=7
9z=-9
z=1

Answer 50

@jim_thompson5910

Answer 51

9z=-9 would not lead to z = 1

however you are very close

Answer 52

then what?

Answer 53

oh -1

Answer 54

yep so we know

y = 6
z = -1

Answer 55

use y = 6 and z = -1 to find x

Answer 56

but i thought we already found x

Answer 57

@mathstudent55 did in terms of x

Answer 58

recall that x = -z+2

Answer 59

yes

Answer 60

plug in z = -1 to find x

Answer 61

how do i do that again

Answer 62

just replace the letter with the value

Answer 63

into which one tho

Answer 64

\[\Large x = -z+2\]
\[\Large x = -1*(z)+2\]
\[\Large x = -1*({\color{red}{z}})+2\]
\[\Large x = -1*({\color{red}{-1}})+2\]
\[\Large x = ???\]

Answer 65

3

Answer 66

@jim_thompson5910

Answer 67

yep so the answer is

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

ie

x = 3
y = 6
z = -1

Answer 68

thank you so much... do you mind helping me with just a few more :)

Answer 69

sure, just make a new post to avoid clutter and lag

Answer 70

ok