Section 4-1

By looking at the graph, we see that the solution is (x,y) = (2,4).

Since the lines are parallel, they never intersect. Therefore the system has NO SOLUTIONS.

Solving the first equation for y gives us  y = 3x - 7.  Now, plugging that into the second equation yields
2x + 3(3x -7) = 1
   2x + 9x -21 = 1
               11x = 22
                    x = 2
Now that we've got a value for x, we plug it back into y = 3x - 7 to find y.  (Plugging it into either
equation of the original system would work just as well.)
y = 3(2) - 7
 y = -1

Thus the solution is (x,y) = (2, -1).

Therefore we get that x = -1. Plugging this back into the second equation (the first would work just as well):
5(-1) + 3y = 1
-5 + 3y = 1
3y = 6
y = 2

Thus (x,y) = ( -1, 2) is the solution.

Since we get a false statement, it's impossible for both equations to be satisfied by the same (x, y).
Thus the system has NO SOLUTIONS.