Unformatted text preview: 4 5 6 7 x
1 3, − 1
2 2 3 4 x −1 −3
−4 x
− 4y
3
5
2x
+y
9
3 2 =7
5
=1
2 2x − 4y = 6
3x − 6y = 9
(Same line.) See Section 1.2 for a review of this.
Note that we could have just as easily chosen to solve 2x − 4y = 6 for x to obtain x = 2y + 3. Letting y be the
parameter t, we have that for any value of t, x = 2t + 3, which gives {(2t + 3, t) : −∞ < t < ∞}. There is no one
correct way to parameterize the solution set, which is why it is always best to check your answer.
3 8.1 Systems of Linear Equations: Gaussian Elimination 453 5. Multiplying both sides of the ﬁrst equation by 2 and the both sides of the second equation
by −3, we set the stage to eliminate x
12x + 6y =
18
+ (−12x − 6y = −36)
0 = −18
As in the previous example, both x and y dropped out of the equation, but we are left with
an irrevocable contradiction, 0 = −18. This tells us that it is impossible to ﬁnd a pair (x, y )
which satisﬁes both equations; in other words, the system has no solution. Graphical...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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