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>