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Eliminate works but Solve does not?

• To: mathgroup at smc.vnet.net
• Subject: [mg121515] Eliminate works but Solve does not?
• From: RobertB <robert.c.baruch at gmail.com>
• Date: Sun, 18 Sep 2011 04:11:06 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

I have a physical problem where I have a system of 9 equations in 10
unknowns. I am trying to determine the relationship between 2
unknowns. Here is the system:

Subscript[y, 3]^2 + Subscript[x, 3]^2 == Subscript[L, 3]^2 &&

 Subscript[y, 1]^2 + Subscript[x, 1]^2 == Subscript[L, 1]^2 &&

 Subscript[x, 1] + Subscript[x, 3] == 2 &&

 Subscript[y, 1] == Subscript[y, 3] - 2 &&

 Subscript[y, 4]^2 + Subscript[x, 4]^2 == Subscript[L, 3]^2 &&

 Subscript[y, 2]^2 + Subscript[x, 2]^2 == Subscript[L, 1]^2 &&

 Subscript[x, 2] + Subscript[x, 4] == 1.6875 &&

 Subscript[y, 2] == Subscript[y, 4] - 2 &&

 Subscript[y, 4] == Subscript[y, 3] + (0.3125/2)

Now, when I use Solve[..., {Subscript[L, 1], Subscript[L, 3]}], the
answer is { }.

However, when I use Eliminate[..., {Subscript[x, 1], Subscript[x, 2],
Subscript[x, 3], Subscript[x, 4], Subscript[y, 1], Subscript[y, 2],
Subscript[y, 3], Subscript[y, 4]}], I get a proper answer, that is, a
function of L_1 and L_3 = another function of L_1 and L_3.

Even if I add a condition, such as Subscript[L, 1] == 1 to the system,
and Solve (or even NSolve) for Subscript[L, 3], I get { } even though
I know that a solution exists.

Can anyone explain why Solve/NSolve doesn't seem to do anything?

Thanks!

• Follow-Ups:
  • Re: Eliminate works but Solve does not?
    • From: DrMajorBob <btreat1@austin.rr.com>
  • Re: Eliminate works but Solve does not?
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>