Question

Solve this system of equations.

Answer 1

Hey, did a similar prob before but the x,y,z is throwing me off a little....

Answer 2

Looks like a good candidate for a matrix.

Answer 3

Yea but how would I find the values of the variables?

Answer 4

By solving the system . . .
:-/

Answer 5

You could also do regular substitution or various other elimination methods.

Answer 6

Alright. I'll try substitution first. Also are the numbers at the far right representing each variable?

Answer 7

i did not understand complete elimination (gauss method)

Answer 8

Do you know a better way to do this?

Answer 9

No, the numbers at the far right are just constants.

Answer 10

You can try substitution first if you're still a little shaky with the matrix method.
A good start would be to solve the first equation for z, and substitute that expression into the second and third equations. Then you can do other substitutions/eliminations to find x and y.

Answer 11

how would I find z?

Answer 12

After you get x and y, go back to the first equation that you solved for z and put in the x,y values.

Answer 13

So I use substitution and only use the 3x+2y=7 part for the substitution?

Answer 14

No, you use 3x+2y+z=7 to solve for z (i.e. get an expression for z in terms of x and y), then sub that expression into the other two equations to eliminate z.

Answer 15

So for this I could do the first equation and the last equation to get: 3x+2y+z=7
-(3x+2y+3z=1)

-3z=1 z=-0.3 (-3/10)

Answer 16

That's a good elimination step, but if you did that you'd get z=3, I believe.

Answer 17

Sorry, -3.

Answer 18

Ohhh srry.

Answer 19

I did get -3 in the beginning guess I did the unesseccary step at the end.

Answer 20

Though by doing this I didn't get x and y values.

Answer 21

No, but now you can sub z=-3 into all your equations, then pick two of them to go about solving for x and y.

Answer 22

So now we have:
3x+2y+-3 =7
5x+5y+(-12) =3
3x+2y+(-9) =1

Answer 23

That looks right. Now you can pick two of those to use to solve for x and y.

Answer 24

and I can solve by doing something like this?: 7-(-3)=3x+2y

Answer 25

You might notice something suspicious about equations one and two now if you hadn't before.

Answer 26

^^ simplifying is always good.

Answer 27

You mean there's something weird other than them cancling eachother?

Answer 28

Nope, them cancelling each other is weird enough. What does that mean though?

Answer 29

They are basically 0's now?

Answer 30

No, those two equations are the same, they represent the same line, so one is a dependent equation and cannot be used.

Answer 31

Oh, so how do we tell which is which?

Answer 32

It doesn't matter, just throw out one of the identical equations and work with the other two.

Answer 33

I simplified 3x+2y+(-3) =7 to 10=3x + 2y and put it with
5x+5y+(-12) =3
But I can't figure it out.

Answer 34

You have two equations in x and y:

3x + 2y = 10
5x + 5y = 15

The second equation can be divided by 5 if you like to reduce it.

Answer 35

Ohhh 1x+1y=3 right?

Answer 36

Yeah. That's optional, but it makes the numbers smaller, which is nice.

Answer 37

Alright then what? x would have to =0 but then y wouldn't match up for both equations :/

Answer 38

Why would x=0? That doesn't follow from either equation.

Answer 39

Couldn't think of how 1x+1y=3 otherwise

Answer 40

In x + y = 3, if x=0, then 0+y=3 and y=3, but this doesn't work with other equation
3x + 2y = 10 --> 3(0) + 2(3) = 6 =/= 10.

Answer 41

I tried it with 1 1/2 but it still doesn't work. =/

Answer 42

Guessing-and-checking is a very slow and often impossible way to solve equations.
I recommend algebra.

Answer 43

Alright so y=-1 and x=4 then?

Answer 44

Yes, those are the solutions; along with z=-3, the solution set is {(4,-1,-3)}

Answer 45

Thanks so much again. =)