How to combine expressions in Maxima?

Following is MACSYMA expressions

eq1: a*x - b*y = 0;
eq2: c*x +d*z = 0;
eq3: y+z = 0;

subst([eq1,eq2],[eq3]);

I am expecting result as a/b = c/d after cancelling common x.

But I did not get expected result. And MACSYMfl also has trouble cancelling a common term from right and left hand sides.

How does one get around this?

Solution

IIUC, what you want is to solve eq1 for y, eq2 for z, and substitute those values into eq3. If I do that by hand, I get

(%i14) solve(a*x-b*y=0,y);

                                        a x
(%o14)                             [y = ---]
                                         b
(%i15) solve(c*x+d*z=0,z);

                                         c x
(%o15)                            [z = - ---]
                                          d
(%i16) %o14+%o15;

                                       a x   c x
(%o16)                        [z + y = --- - ---]
                                        b     d

And since z+y = 0, a*x/b-c*x/d is zero, which produces your desired a/b=c/d.

One way of doing this is to use eliminate:

(%i24) eliminate([eq1,eq2,eq3],[y,z]);
(%o24)                         [- (b c - a d) x]

Setting this to zero gives b*c-a*d is zero, which is equivalent to your expected a/b=c/d.