1. **State the problem:** Find two integers $x$ and $y$ such that $x - y = 4$ and their squares differ by 72, i.e., $x^2 - y^2 = 72$. 2. **Use the difference of squares formula:** $x^2 - y^2 = (x - y)(x + y)$. 3. Given $x - y = 4$, substitute this into the difference of squares equation: $$x^2 - y^2 = (4)(x + y) = 72$$ 4. Solve for $x + y$: $$4(x + y) = 72 \\ x + y = \frac{72}{4} = 18$$ 5. Now we have a system of linear equations: $$\begin{cases} x - y = 4 \\ x + y = 18 \end{cases}$$ 6. Add the two equations to eliminate $y$: $$ (x - y) + (x + y) = 4 + 18 \\ 2x = 22 \\ x = 11 $$ 7. Substitute $x = 11$ into $x - y = 4$: $$ 11 - y = 4 \\ y = 11 - 4 = 7 $$ **Answer:** The two integers are $11$ and $7$. These satisfy: - Difference: $11 - 7 = 4$ - Squares difference: $11^2 - 7^2 = 121 - 49 = 72$