Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 3 - Section 3.1 - Systems of Linear Equations in Two Variables - Exercise Set - Page 190: 20

Answer

$(1,-5)$.

Work Step by Step

First equation $4x-y=9$. Plug $y=0$ into the equation. $4x-0=9$ $4x=9$ $x=\frac{9}{4}$ $x-$ intercept $A=(\frac{9}{4},0)$. Plug $x=0$ into the equation. $4(0)-y=9$ $0-y=9$ $y=-9$ $y-$ intercept $B=(0,-9)$. Now for the second equation $x-3y=16$. Plug $y=0$ into the equation. $x-3(0)=16$ $x+0=16$ $x=16$ $x-$ intercept $C=(16,0)$. Plug $x=0$ into the equation. $0-3y=16$ $0-3y=16$ $-3y=16$ $y=-\frac{16}{3}$ $y-$ intercept $D=(0,-\frac{16}{3})$. Draw two lines using intercept points. Graph is shown below in the image. The intersection point of both lines is the solution. Here we have the intersection point at $(1,-5)$.
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