Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 1 - Systems of Linear Equations - 1.1 Introduction to Systems of Linear Equations - 1.1 Exercises: 77

Answer

We have to choose $k=-2$.

Work Step by Step

Step 1: Make the right sides of the equations equal. This can be done by multiplying the second equation by $-2$: \begin{align*} 4x+ky=&6\\ -2kx-2y=&6 \end{align*} Step 2: Now since we want infinitely many solutions we want that the left sides of the equations be identical (same coefficients multiplying $x$ and $y$) so that we really have only one independent equation. If we choose $k=-2$ this will be the case because then we will have: \begin{align*} 4x-2y=&6\\ 4x-2y=&6 \end{align*} which is what we wanted.
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