Thread: multiple unknowns

Let's say I have 3 equations:

s = y + d * r
r = b + d * q
q = x + d * m

Let's say d, q, and r are unknown.

Is it possible to solve for d?

Originally Posted by Nickmare

Let's say I have 3 equations:

s = y + d * r
r = b + d * q
q = x + d * m

Let's say d, q, and r are unknown.

Is it possible to solve for d?

Yes.

replace q in the 2nd equation with the 3rd.

r = b + d * ( x + d * m )

replace r in the 1st equation by the above

s = y + d * ( b + d * ( x + d * m ) )

simplify:

s = y + d*b + d^2 * x + d^3 * m

thus:

d^3 * m + d^2 * x + d*b + y - s = 0

1 equation, 1 unknown.