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

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?

[madhan ravi]

"I want to be able to solve for a in terms of b,c,d; hence eliminating e from these equations."

please explicitly state how your result should look like

[Kaden Penner]

I have updated the question.

Answer 1

[Walter Roberson]

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

[Kaden Penner]

Thanks a ton!