Let's start by rewriting the given equations in slope-intercept form, this way we can have a first look and see if the equations represent the same line, and then an infinite number of solutions are present.
We can rewrite the equations in slope-intercept form by solving for y, like this:
For the first equation, -3x + y = 22:
-3x + y = 22
-3x + 3x + y = 22 + 3x
y = 22 + 3x
y = 3x + 22
For the second equation, -9x + 3y = 66
-9x + 3y = 66
-9x + 9x + 3y = 66 + 9x
3y = 66 + 9x
3y/3 = 66/3 + 9x/3
y = 22 + 3x
y = 3x + 22
As you can see, both equations look the same (y = 3x + 22) in slope-intercept form. Since they represent the same line the system of linear equations will have an infinite number of solutions.
