Question

Solve the system by the method of substitution.

2x-2y-z=-14
z=-8
2x+3y+3z=-6

Answer 1

@vinnv226

Answer 2

@blurbendy

Answer 3

Hmm, I would start by plugging in -8 for all the "z"s in the first and third equations, and then simplify. Since you know the value of a variable right off the bat, it makes sense to plug it in and make the other equations simpler

Answer 4

kk

Answer 5

so when i pluged it in for the first equation i got 2x-16-8=-14

Answer 6

is that wrong

Answer 7

You plugged in -8 for the y and the z. You can only plug it in for "z" because thats what the second equation tells us. We don't know what y is yet

Answer 8

kk

Answer 9

2x-2y=6

Answer 10

Yep, exactly. So now plug in z=-8 to the third equation as well

Answer 11

kk

Answer 12

2x+3y=18

Answer 13

@vinnv226

Answer 14

for the first equation, if you substituted -8 in for z you should get:

2x - 2y - (-8) = -14

2x - 2y + 8 = -14

2x - 2y = -22

Answer 15

o did i do the second right

Answer 16

* second one

Answer 17

yup, looks good

Answer 18

kk what do i do know

Answer 19

you can solve for another variable. for example, the second equation says:

2x+3y=18

so you could solve for x

Answer 20

Yea, the first one was incorrect, and I didn't notice it. My mistake

Answer 21

lol im confused

Answer 22

no problem

Answer 23

you could solve for x for 2x+3y=18

you would start by subtracting 3y from both sides

2x = -3y + 18

Answer 24

kk

Answer 25

you have get x by itself though, so what do you do with the 2 in front?

Answer 26

okay i got 2x=15 now divide by 2 to get it by itself right

Answer 27

you can't add -3y and 18, the -3 is multiplied by y, so you can't add it to 18.

but yes, you would divide by 2

x = -3/2y +18/2

x = -3/2y + 9

Answer 28

lol sry

Answer 29

so know what do i do with the -3/2y add it

Answer 30

no, we know x = -3/2y + 9 now, so we can substitute x in the first equation we found:

2x - 2y = -22

2(-3/2y + 9) -2y = -22

Answer 31

-6y+18-2y=-22

Answer 32

not quite,

2 * -3/2 = -3 the two's cancel

so you end up with:

-3y + 18 - 2y = -22

Answer 33

kk know do i add 2y to each side

Answer 34

you dont need to, you can just add -3y -2y first

Answer 35

what does that give you?

Answer 36

wait i add them so they cancel but what about the other side will it be 18=-22+2y+3y

Answer 37

add them toghehter u mean

Answer 38

no, i meant you can just evaluate -3y -2y on the same side first:

-3y - 2y + 18 = -22

-5y + 18 = -22

Answer 39

8

Answer 40

yes, now you know y = 8

we know y = 8
z = -8

so to find x we can just look at the first equation and solve for x:

2x - 2(8) -(-8) = -14

Answer 41

x=2

Answer 42

2x -16 + 8= -14

2x -8 = -14

2x = -6

so what does x equal

Answer 43

sry i got 20 its 22 added wrong answer -3

Answer 44

yes, x = -3

Answer 45

so, z = -8
y = 8
and x = -3

Answer 46

we are done!

Answer 47

thank you

Answer 48

anytime