Question

Solve the system of equations:

2x+y-z=-5
4x-2y+z=10
2x+3y+2z=3

Answer 1

@johnweldon1993

Answer 2

Any ideas how to start?

Answer 3

Um, I guess there are multiple ways to start. After doing this problem a million times, I still couldn't get the third equation to agree with the rest. But I guess we can isolate the z.
So if we take the first equation and isolate the z, it would be z=2x+y+5

Answer 4

Oh good you already worked it!

Alright let's go through it and see what went off :)

Good first step...next?

Answer 5

Okay, then we would plug it into the second equation right?
4x-2y+2x+y+5=10

Answer 6

6x-y=5
Good so far?

Answer 7

Looks good

Answer 8

Um, we can isolate the y.
y=6x-5

Answer 9

I don't know what would be the best thing to do from here.

Answer 10

Okay from there *NOT isolating the 'y' * we don't want to further manipulate that equation we have

\[\large 6x - y = 5\]

From here...take your 'z' you isolated using the first equation....and now plug that in for the 'z' ALSO in the third equation

Answer 11

Because in a system of 3 equations...your first goal should be to get it down to 2 equations and 2 unknowns

Answer 12

Oh, i see.

Answer 13

Alright.
2x+3y+2(2x+y+5)=3
6x+5y=7

Answer 14

Oh, we can do 7-5y=5+y right?

Answer 15

Re-check that real quick :)

Answer 16

-7, my bad.

Answer 17

Would it work if I do
-7-5y=5+y
Cause they both have 6x.

Answer 18

There we go...so we are down to 2 equations

\[\large 6x - y = 5\]
\[\large 6x + 5y = -7\]

And you're right that WOULD work! So what do you get for 'y' then?

Answer 19

Wait, let me write this down :P

Answer 20

-6y=12
y=-2

Answer 21

Awesome!

Now use that to get your 'x'

Answer 22

Do I plug it into all the equations?

Answer 23

Not yet...so we went from 3 equations

to 2 equations

to 1 --> we solved for 'y'

Now work backwards, back to the 2 equations, and plug in that 'y' and solve for 'x'

Answer 24

Reason being, if you plug in 'y' into the original 3 equations, you'll have too much to do to simplify...easier to just work backwards now :)

Answer 25

Oh, okay.
So umm,
4x-2(-2)+2x+-2+5=10
4x+4+2x-2+5=10
6x+7=10
6x=3
x=.5

Answer 26

And z should be 4.

Answer 27

Haha you could have worked with the simplified ones :)

\[\large 6x-y=5\]
\[\large 6x + 5y = -7\]

Regardless, correct...x = 1/2

NOW you have both ...

nvm beat me to it...it is indeed lol

Answer 28

There you go!

Answer 29

Thank you very much. I spent all my free periods trying to finish this up. I appreciate it!

Answer 30

Not a problem!