Half of the difference between two numbers is 2. The sum of the greater number and twice the smaller number is $\displaystyle 13$ . Find the numbers.

Let the numbers be x and \(\displaystyle \mathrm{y}, \mathrm{x}>\mathrm{y}\) Therefore \(\displaystyle \frac{1}{2}(\mathrm{x}-\mathrm{y})=2 \quad\) - (i) and \(\displaystyle 2 \mathrm{y}+\mathrm{x}=13\) - (ii) Solving equations (i) and (ii) \[x=7, y=3 \]