Limited scope of
The only thing you are doing wrong is to have expectations beyond the capability of
You get the warning
Eliminate::ifun: Inverse functions are being used by Eliminate, so
some solutions may not be found; use Reduce for complete solution
The documentation reads :
Eliminate works primarily with linear and polynomial equations.
Eliminate will work with complicated expressions, but it's only supposed to work with polynomial equations. Other tools like
Reduce sometimes will not find solutions either.
Borrowing from @Nasser in the comments, you can solve for
j on one equation and replace on the other. Notice there are two solutions, so I
Or to keep this as a single logical expression.
y == h/2 + j/2*Sin[j/50 - t/50 - i/118] + (i*9/10)* Cos[j/25 - (i + t)/65]
, Echo[Solve[ x == 10*Sin[i/10] + j + 8/1000*j*j - 30, j], "Solutions:", Length]
jinstead of the first one? Manually, you can do it as follows
eq1 = x == 10*Sin[i/10] + j + 8/1000*j*j - 30; eq2 = y == h/2 + j/2*Sin[j/50 - t/50 - i/118] + (i*9/10)* Cos[j/25 - (i + t)/65]; solJ = Solve[eq1, j]; eq2 /. solJwhich eliminates
j. Screen shot !Mathematica graphics $\endgroup$
Eliminateis not supposed to be used with non-linear equations. $\endgroup$