Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 3 - Section 3.1 - Systems of Two Equations in Two Unknowns - Exercises: 11

Answer

$(\displaystyle \frac{1-3y}{2}, y)$

Work Step by Step

Remove the fractions by multiplying the second equation with $2$, (common denominator). $\left\{\begin{array}{llll} 2x & +3y & =1 & \\ -2x & -3y & =-1 & /\times 4 \end{array}\right.$ ... add to eliminate x, solve for y... $0=0$ $y$ can be ANY real number (the system is consistent, but there are infinitely many solutions) (we expect the graphs to be the same) Express x in terms of y from any of the initial equations: $2x+3y=1\qquad/-3y$ $2x=1-3y\qquad/\div 2$ $x=\displaystyle \frac{1-3y}{2}$ solution: $(\displaystyle \frac{1-3y}{2}, y)$ Check graphically by graphing both lines in the same window and confirming that both equations have the same graph (see image).
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.