Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 4 - Section 4.1 - Solving Systems of Linear Equations by Graphing - Exercise Set - Page 292: 48


a. The lines intersect at a single point. b. The system has one solution.

Work Step by Step

$2y=x+2=\gt m=1$ $y+2x=3 =\gt m=2$ You can find out the slope of each of the equations by just looking at it. The slope is the number thats multiplied by $x$. Based on the slope you can find out if the graphs of the equations are identical lines, parallel lines, or lines intersecting at a single point. Parallel and and identical lines have the same slope, which in this case is not true. This means that the lines must intersect at a single point and therefore has only one solution. The solution of two equations shows the intersecting point. One solution means one intersecting point. No solution means no intersecting point, which is true for parallel lines. And an unlimited amount of solutions means that the lines intersect in every point and are identical.
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