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# Consistent or Inconsistent Equation? (FP2) watch

1. 3x-7y=3
2x+2y+5z=2
x+3y+4z=1

given that there were no unique solutions to these equations,I manipulated them to get

4y-3z=0
and
4y+3z=0

I'm confused whether these are consistent or inconsistent, and how to geometrically interpret the three planes ?

any help would be great!
2. (Original post by F3rnw3h)
3x-7y=3
2x+2y+5z=2
x+3y+4z=1

given that there were no unique solutions to these equations,I manipulated them to get

4y-3z=0
and
4y+3z=0

I'm confused whether these are consistent or inconsistent, and how to geometrically interpret the three planes ?

any help would be great!
Do

4y-3z=0
and
4y+3z=0

have a solution?

Two equations are inconsistent when you have 4x+3y =1, and 4x+3y=6, for example. The "4x+3y" has to simultaneously have two values - which isn't possible, and then they are inconsistent.

Edit: I don't know how you arrived at that point, but suspect you've made an error further back, but depends on what you think the final solution is.
3. (Original post by F3rnw3h)
3x-7y=3
2x+2y+5z=2
x+3y+4z=1

given that there were no unique solutions to these equations,I manipulated them to get

4y-3z=0
and
4y+3z=0

I'm confused whether these are consistent or inconsistent, and how to geometrically interpret the three planes ?

any help would be great!
pretty sure you've made an error somewhere, can you show your working?
4. (Original post by ghostwalker)
Do

4y-3z=0
and
4y+3z=0

have a solution?

Two equations are inconsistent when you have 4x+3y =1, and 4x+3y=6, for example. The "4x+3y" has to simultaneously have two values - which isn't possible, and then they are inconsistent.

Edit: I don't know how you arrived at that point, but suspect you've made an error further back, but depends on what you think the final solution is.
Thankyou! I'd made a sign error somewhere. But now I know that the equations are consistent, how do I know whether the planes form a sheaf or all the planes coincide?
5. (Original post by _gcx)
pretty sure you've made an error somewhere, can you show your working?
You're right, I made a sign error -thanks!
6. (Original post by F3rnw3h)
Thankyou! I'd made a sign error somewhere. But now I know that the equations are consistent, how do I know whether the planes form a sheaf or all the planes coincide?
have you found a finite or infinite set of solutions? also, you know that the planes are distinct and hence don't "coincide".
7. (Original post by _gcx)
have you found a finite or infinite set of solutions? also, you know that the planes are distinct and hence don't "coincide".
Thanks! Would you have an example of what a set of coinciding planes look like?
8. (Original post by F3rnw3h)
Thanks! Would you have an example of what a set of coinciding planes look like?
a simple one would be x+y+z = 1, 2x+2y+2z = 2, 3x+3y+3z=3.
9. (Original post by _gcx)
a simple one would be x+y+z = 1, 2x+2y+2z = 2, 3x+3y+3z=3.
Thankyou! Makes more sense now

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