Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Appendix B - Coordinate Geometry and Lines - B Exercises - Page A16: 57


The lines intersect at the point $(1,-2)$

Work Step by Step

The linear equations are not parallel because they do not have the same slope. The slope can be seen by looking at the coefficient of the "$x$-term," and for one equation it is 2 and the other 3. To find the point of intersection, isolate each equation for $y$: $2x-y=4\qquad\qquad6x-2xy=10$ $y=2x-4\qquad\qquad2y=6x-10$ $\qquad\qquad\qquad\qquad\quad y=3x-5$ Now set each equation equal to itself to solve for $x$: $2x-4=3x-5$ $1=x$ Now plug $x=1$ back into either equation to find the corresponding value of $y$: y=2(1)-4 = 2-4 y=-2 Therefore the point of intersection is $(1,-2)$
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