[**Hint:** you may wish to start by multiplying the second equation by \(x+y\).]

Find all values of \(a\), \(b\), \(x\) and \(y\) that satisfy
\[\begin{align*}
a+b &= 1 \\
ax+by &= \frac{1}{3} \\
ax^2+by^2 &= \frac{1}{5} \\
ax^3+by^3 &= \frac{1}{7}.
\end{align*}\]

[**Hint:** you may wish to start by multiplying the second equation by \(x+y\).]