Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 10 - Section 10.5 - Equations of Lines - Exercises - Page 481: 49

Answer

$a=5~~$ and $~~b=2$

Work Step by Step

We can multiply the first equation by 2: $6x-4y=38$ We can multiply the second equation by -3: $-6x+15y=-27$ We can add the two equations: $-4y+15y = 11$ $11y = 11$ $y = 1$ We can use the first equation to find the x-coordinate: $3x-2y = 19$ $3x-2(1) = 19$ $3x-2 = 19$ $3x = 21$ $x=7$ The point of intersection is $(7,1)$ The point of intersection is $(a+b,a-2b)$ Then: $a+b = 7$ $a-2b = 1$ We can subtract the second equation from the first equation: $3b = 6$ $b = 2$ Since $a+b=7$, then $a=5$ $a=5~~$ and $~~b=2$
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