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

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:

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.

in geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. by extension, a line and a plane, or two planes, in three-dimensional euclidean space that do not share a point are said to be parallel.

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