MATLAB: Is there a way to specify independent variables when solving symbolic equations

equationsMATLAB

Lets say I have a set of X equations with Y>X symbolic variables defining relations between several dependent and independent variables:
syms a b c d e
eq1 = a + 3*c == b*2 - 5*e - d;
eq2 = b - 2*a == e;
eq3 = d - 2*b == 10*a - e;
I want to be able to solve for a in terms of b,c,d; hence eliminating e from these equations.
When I do:
solve(eq1,eq2,eq3)
It returns:
  struct with fields:
    c: [1×1 sym]
    d: [1×1 sym]
    e: [1×1 sym]
I have tried:
    solve(eq1,eq2,eq3,a)
But it gives an empty symbol:
    Empty sym: 0-by-1
But from the equations above, it is clear that a could be described solely in terms of b,c,d.
I want the result of this to be:
    a = M*b + N*c + P*d
Is there a way to do this in Matlab?

Best Answer

Except for some cases involving inequalities, you need to solve for the same number of variables as you have equations. And the inequalities case fails a lot of the time anyhow.
You are trying to solve three equations for 1 variable. You cannot do that.
What you can do is
sol = solve( subs([eq1, eq2], e, solve(eq3,e)), [a b])
This will give you sol.a and sol.b in terms of c and d
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