Hello, fancyface!

Choose two different positive numbers.

Then construct a system of two linear equations with two variables,

such that its solution consists of exactly the two chosen numbers.

Explain your method of creating the system.

As a teacher, I've done this many many times.

First, I make a "skeleton" of the problem.

. .

Then I select values for and . . . say,

Plug them into the skeleton and determine and .

. .

Then the system: . has the solution:

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

We can make the answers as hard as we like: .

Using the skeleton: .

Then: .

Therefore: . has the solution: