``````Section 4-1
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 (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 yields2x + 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 eitherequation 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.