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 - Page 185: 11


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

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).
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