Question

Solve the system
-3x+y+3z=-2
x+7y-2z=5
4x+6y-5z=7
Please help

Answer 1

in what way you want to solve it?

Answer 2

If it is consistent, inconsistent, or dependent.

Answer 3

Okay, I have found it to be dependent but how do I find x and y?

Answer 4

let z=k and write first two equations in terms of x and y and k
then find x and y in terms of k.

Answer 5

What is k?

Answer 6

k is an arbitrary constant.

Answer 7

So if I was to use x+7y-2z=5 to find x how would I do it?

Answer 8

then you will find x and y in terms of z.

Answer 9

I still don't get it

Answer 10

Split the system into pairs. Then eliminate the same variable from each pair. Afterwards what you will end up with is a system of two equations, which you should be able to solve.

Answer 11

I did that and 0=0 but I still have to find x and y

Answer 12

a) -3x+y+3z=-2
b) x+7y-2z=5

c) x+7y-2z=5
d) 4x+6y-5z=7

Answer 13

Right and I ended up with
-22y+3z=-13
22y-3z=13

Answer 14

Multiply both sides of equation b) by -3
Multiply both sides of equation c) by 4


a) -3x+y+3z=-2
b) -3x-21y +6z=-15

c) 4x+28y-8z=20
d) 4x+6y-5z=7

Then eliminate the x variable to get:

22y -3z = 13
22y -3z = 13

Answer 15

Was I wrong to multiply by 3 and -4?

Answer 16

Not necessarily, but you should have ended up with what I got.

Answer 17

I did. But I ended up with the equations canceling out and 0=0

Answer 18

Nevermind. It really doesn't matter. Either way, you end up with 0 = 0

Answer 19

Basically, it is not possible to solve for y or z.

Answer 20

Well, my assignment says if the answer is dependent I have to express the solution in terms of one of the variables.

Answer 21

It is supposed to look like this {(numbers, numbers, variable)|(epsilon)R}

Answer 22

Try using matrices to figure it out

Answer 23

What?

Answer 24

If you've never heard of matrices, then disregard

Answer 25

-3x+y=-2-3z ...(1)
x+7y=5+2k ...(2)
multiply (2) by 3 and add in (1)
22y=13+3ky
\[y=\frac{ 13+3k }{ 22 }\]
similarly x=?
solution is x=?
\[y=\frac{ 13+3k }{ 22 }\]
z=k
giving different values to k we get different values of x,y,z.