Section 4-1
(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 | |
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|
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 | |
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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.