Postage stamps

A collector buys \(40\) postage stamps. Each stamp costs either \(\$0.50\) or \(\$1.10\), and the total cost is \(\$31.40\). Let \(x\) be the number of \(\$0.50\) stamps and \(y\) be the number of \(\$1.10\) stamps.

1. Write down two equations connecting \(x\) and \(y\).
2. Hence, solve the simultaneous equations obtained in (a) and find the number of stamps of each value.