# Direct solution for two unknowns in two equations

#### IanfromBristol

##### New member
I am writing a computer program to solve a physical problem which at some part involves the following two equations and two unknowns;

(1) $C_1(x^4-y^4) + C_2x = Q_1$
(2) $C_1(y^4-x^4) + C_3y = Q_2$

C1, C2 & C3 are coefficients which can readily be calculated and do not rely on knowing the values of X or Y. Q1 and Q2 are known values (effectively boundary conditions). I've tried substitution and elimination but end up with a much more complicated expression which looks to be a quartic equation. I know I can solve this iteratively and it does converge quickly and is stable. However, is there any method that can solve it directly and thus avoid the iterative approach?

#### topsquark

##### Well-known member
MHB Math Helper
I see no way to avoid the quartic. There is a method to do this to get an exact answer (here) but I'd stick with approximation. It's much easier to work out.

-Dan

#### IanfromBristol

##### New member
I see no way to avoid the quartic. There is a method to do this to get an exact answer (here) but I'd stick with approximation. It's much easier to work out.

-Dan
Hi Dan, I took a look at that solution for the quartic and you're not wrong the iterative method (i.e. approximation) is far easier to work out!

Ian

• topsquark