### Instruction: The sum of two numbers is $19$ and their difference is $5$. What is their product?### Response: I need to find two numbers that add up to $19$ and subtract to $5$.
I can try to guess and check, but that might take a long time.
I can also try to use algebra and solve a system of equations.
Let me call the two numbers $x$ and $y$.
Then I have $x + y = 19$ and $x - y = 5$.
I can add these two equations and get $2x = 24$, so $x = 12$.
Then I can plug $x = 12$ into either equation and get $y = 7$.
So the two numbers are $12$ and $7$.
To find their product, I just multiply them together: $12 \times 7 = 84$.