How to combine expressions in Maxima?

Question

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?

Answer 1

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.