Please solve −3x−y=6 |

To solve linear equations, they may have no solutions, one solution, or infinite solutions.

Given this is a linear equation with two variables, it would have infinite solutions.  Another reason it would be called a "linear solution" would be because all of the solutions would be represented by a straight line (an infinite set of points).  So, the difficult part is, what are the points?

For that, y depends upon what x is (or vice versa).  So, x could be almost anything, and y could be almost anything.  But, as x changes, y would change as well (and vice versa).

To solve this equation, then, what you would need to do is substitute a number in for x, then solve for y.  Any number will do.  Some numbers are easier than others.  For instance:

If x = 0, then -3*0 - y = 6

0 - y = 6

-y = 6

y = -6

So, one solution would be (0,-6)

Also, we could plug in something for y and solve for x.  For instance:

If y = 0, then -3x - 0 = 6

-3x = 6

x = -2

So, one solution would be (-2,0)

You would plot these two solutions on an x-y coordinate plane, then draw the straight line connecting these two points.