Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 7 - Algebra: Graphs, Functions, and Linear Systems - 7.3 Systems of Linear Equations in Two Variables - Exercise Set 7.3 - Page 445: 40

Answer

Infinitely many solution and the solution set is\[\left\{ \left( x,y \right),y=3x-4 \right\}\]or\[\left\{ \left( x,y \right),9x-3y=12 \right\}\].

Work Step by Step

Substitute\[y=3x-4\]in the equation\[9x-3y=12\] to get: \[\begin{align} & 9x-3\left( 3x-4 \right)=12 \\ & 9x-9x+12=12 \\ & 12=12 \end{align}\] Since\[12=12\], it implies the system of the equation having infinitely many solutions. The line coincide and all the points lying on the lines are the solution to the system of equation. The set of solutions is\[\left\{ \left( x,y \right),y=3x-4 \right\}\]or\[\left\{ \left( x,y \right),9x-3y=12 \right\}\].
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