Question

The sum of two numbers is 42 and the difference is 4. What are the numbers?

Answer 1

Define a system of equations that describes the given situation.

Take x and y as the numbers.

$\begin{gathered} x+y=42 \\ x-y=4 \end{gathered}$

Solve the system:

$\begin{gathered} x+y=42 \\ x=42-y \\ x-y=4 \\ x=4+y \\ 42-y=4+y \\ 42-4=2y \\ 38=2y \\ y=\frac{38}{2} \\ y=19 \end{gathered}$

Use the value of y to find the value of x.

$\begin{gathered} x=4+y \\ x=4+19 \\ x=23 \end{gathered}$

Which means that the numbers are 23 and 19.