Question 69530
Given:
{{{6x - (3/2)y - 12 = 12}}}

Let's begin by simplifying the equation.  Let's multiply everything by 2 to get rid of the denominator in the y-term.

{{{12x - 3y - 24 = 24}}}

Now add 24 to both sides to move the -24 to the right side of the equal sign.

{{{12x - 3y = 48}}}

Now all you have to do is to assume a value for x and find a corresponding value for y.  For example, let's assume x = 1.  The equation becomes:

{{{(12*1) - 3y = 48}}} 

and this becomes:

{{{12 - 3y = 48}}}

Subtract 12 from both sides to get:

{{{ -3y = 36}}}

and by dividing both sides by -3 you find that y = -12

In the Cartesian point form (x,y) this means that (1, -12) is an answer.

You can find other answers using the same process as above.  For example, if you assume x = 2 and substitute that into the equation, you should find that y = -8 so that (2, -8) is another solution.  And if you assume x = 4, you should find that y must = 0 so that (4, 0) is another solution.

Another way to look at this is graphically.  Return to the equation:

{{{12x - 3y = 48}}}

First set x = 0 and the result will be y = 48/-3 = -16.  Plot the point (0, -16) on the graph.  Then let y = 0 and the result will be x = 48/12 = 4.  Plot the point (4, 0) on the graph.  Draw a line through those two points and extend the line in both directions.  Any Cartesian point on that line will give you a set of x and y values that satisfies the equation.  There are any number (an infinite amount) of values that will answer the problem.

Hope this helps you understand the problem a little better.