Seems to me like it's a standard system of equations, just with a lot more to keep track of and a lot more ways to get bogged down in all the details. That said, there's four equations in four variables, so you can solve it in whatever usual way you use to solve systems of equations. For a problem like this, I prefer to use substitution and elimination. Let's start with just the first equation and see what we can come up with:

\(\displaystyle ax + by = 3 \implies ax = 3 - by \implies x = \dfrac{3 - by}{a}\)

That seems promising. What if we plugged that into the second equation?

\(\displaystyle a\left(\dfrac{3 - by}{a}\right)^2 + by^2 = 7 \implies \dfrac{(3 - by)^2}{a} + by^2 = 7 \implies \cdots\)

You try finishing this part here and see what you get. At the end of this step, I'd managed to find an expression for *a* in terms of the only *b* and *y*, which I could then plug into the expression for *x* and simplify it some. Where does all this lead you? What do you think you'd do next?