Please solve −3x−y=6

Please find the attachment for the answer.
I have used Gauss elimination method to solve the equation.

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 = -6So, 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 = -2So, 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.

How to solve -3x-y=6:
To solve an equation is to find all of the values for the variables that make the equality a true statement. A linear equation in one variable will have either no solutions, exactly 1 solution, or an infinite number of solutions.
Here, though, we have a linear equation in two variables. A linear equation in two variables always have an infinite number of solutions; graphically the solutions lie along a line.
We can solve the equation -3x-y=6 for y (or solve for y in terms of x.) This is equivalent to putting the equation in function form as f(x)=y. To solve for y, we need to isolate the y. So we first add 3x to both sides of the equation. (Here we use the addition property of equality.) We will then have -y=3x+6. We wanted to solve for y, not -y, so multiply both sides of the equation by -1 to get y=(-1)(3x+6) or y=-3x-6.
Solving -3x-y=6 for y yields y=-3x-6.
The solutions to the equation are all of the points that lie on the line y=-3x-6. Here is the graph:

Some of the points include (-2,0),(0,-6),(1,-9) etc...
Note that -3x-y=6 is one form of the line; others include the standard form 3x+y=-6, general form 3x+y+6=0, and intercept form x/(-2)+y/(-6)=1 .