Question

Find an ordered pair (x,y) that is a solution to the equation x-6y=6

Answer 1

Since this equation has infinite solutions (each pair is a point on the line with equation x-6y=6), you can choose an arbitrary value for x, say 0, and deduce y:

$0-6y=6 \iff 6y=6 \iff y=1$

So, (0,1) is an ordered pair (x,y) that is a solution to the equation x-6y=6.

You can repeat this process with every possible x value, and solve for the correspondent y value and find infinite pairs.