Section 41
(5) Solve by graphing:  {  3x  y = 2  
x + 2y = 10 
By looking at the graph, we see that the solution is (x,y) = (2,4).
(8) Solve by graphing:  {  3u + 5v = 15  
6u +10v = 30 
Since the lines are parallel, they never intersect. Therefore the system has NO SOLUTIONS.
(12) Solve by substitution:  {  3x  y = 7 
2x + 3y = 1 
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).
(14) Solve by addition:  {  2x  3y = 8 
5x + 3y = 1 
Adding the equations:  2x  3y = 8 
5x + 3y = 1  


7x = 7 
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.
(24) Solve by addition:  {  2x +4y= 8 
x + 2y = 4 
Add 1st to 2 times 2nd:  2x +4y = 8 
2x 4y = 8  


0 = 16 
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.