Question

Solve the following system of equations:

x + y − 4z = −7
2x + 3y − 3z = −6
2x + 2y − z = 0

Answer 1

@jdoe0001

Answer 2

do you know how to solve "system of equations" with 2 variables?

Answer 3

yah substitute but I don't know how to do it with 3

Answer 4

have you done solving by elimination yet?

Answer 5

yes

Answer 6

ok

Answer 7

lemme use the elimination... one sec

Answer 8

the way it works is, we pick 2 off the set of 3
then we eliminate one of the variables

then we pick another 2 off the set, and do the same

so let me pick these two for now \(\bf {\color{brown}{ bx + y - 4z = -7 \\
2x + 3y - 3z = -6}}\\ 2x + 2y - z = 0 \)

\(\large \begin{array}{llll}
x + y - 4z = -7 & {\color{red}{ \times -3}}\to &-3x-3y\cancel{ +12z }=+21\\
2x + 3y - 3z = -6&{\color{red}{ \times 4}}& 8x+12y\cancel{ -12z }=-24\\
\hline\\
&&{\color{blue}{ 5x+9y=\qquad -3}}
\end{array}\)

Answer 9

ok then?

Answer 10

ok then the last 2

Answer 11

then you grab the "resultant 2 equations" and solve for either "x" or "y" to get the other
\(\bf {\color{blue}{ 5x+9y=-3\\
9x-7y=-7}}\)

Answer 12

wait im confused -.- could you show me or tell me what to do? like add them or get x or y by itself to substitute?

Answer 13

hmmm
actually I missed something.... the -4 should give use -8x

Answer 14

\(\large \begin{array}{llll}
x + y - 4z = -7 && x + y \cancel{ - 4z } = -7\\
2x + 2y - z = 0 &{\color{red}{ \times -4}}\to &-8x-8y\cancel{ +4z }=0\\
\hline\\
&&{\color{blue}{ -7x-7y=\qquad -7}}
\end{array}\)

Answer 15

well notice how I added those 2 there


is just a straight forward vertically, once you have the "x" and "y" an "z" all lined up vertically
then you add them vertically :)

Answer 16

so then how do you solve?

Answer 17

so the 2 resultant equation will be \(\bf 5x+9y=-3\\ -7x-7y=-7\)

Answer 18

well use the elimination method

Answer 19

just find 1 of the variables firstly, say "x" or "y"

Answer 20

so 2x+2y=-10 which would be lets say y=-x-5?

Answer 21

using substitution, yes

Answer 22

hmmm

Answer 23

where did we get 2x+2y=-10 again?

Answer 24

^^^ from subtracting the last 2 equations you posted

Answer 25

the ones that you'd need to solve will be the "resulting equations" from the elimination

or
5x + 9y = -3
-7x -7y = -7

Answer 26

ohh .. I see

Answer 27

yea.. that equation should also be workable to find "x" or "y"

Answer 28

so if y = -x-5 then substituting that on either equation

say the 5x+9y=-3 then \(\bf {\color{brown}{ y}}=-x-5\qquad
5x+9{\color{brown}{ y}}=-3 \to 5x+9{\color{brown}{ (-x-5)}}=-3\)

Answer 29

so -5x^2-25x-9x-45=-3?

Answer 30

I honestly don't know like how to solve this an its due at 6:30 :(

Answer 31

and I just have 2 left... do you think we can do the second one?

Answer 32

well... you can always post anew... .if I dunno someone else may, and we can also revise each other