Question

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

Answer 1

The ordered pair (12, 1) is a solution of the equation

How to find a solution?

Express y in terms of x: Rearrange the equation to isolate y:

x-6y=6

y = (x - 6) / 6.

Assign different values to x:

Try substituting different integer values for x and calculating the corresponding y. For example, if x = 12, then y = (12 - 6) / 6 = 1.

Check if the pair satisfies the original equation: Check if the obtained pair (x, y) = (12, 1) satisfies the original equation: 12 - 6(1) = 6, which holds true.

Answer 2

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.