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 294: 69

Answer

Since the point $(-2, 3)$ is a solution of the three equations, all three equations intersect at this one point.

Work Step by Step

$x+y=1$ $x+y-x=1-x$ $y= -x+1$ $y=0$ $x+y=1$ $x+0=1$ $x=1$ This line has a slope of -1, an x-intercept of 1, and a y-intercept of 1. $2x-y=-7$ $2x-y+y+7=-7+y+7$ $2x+7=y$ $y=0$ $2x-y=-7$ $2x-0=-7$ $2x=-7$ $2x/2= -7/2$ $x=-7/2$ This line has a slope of 2, an x-intercept of -7/2, and a y-intercept of 7. $x+3y=7$ $x+3y-x=7-x$ $3y=-x+7$ $3y/3=(-x+7)/3$ $y= -1/3*x+7/3$ $y=0$ $x+3y=7$ $x+3*0=7$ $x+0=7$ $x=7$ This line has a slope of -1/3, an x-intercept of 7, and a y-intercept of 7/3.
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