Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 9 - Systems and Matrices - 9.1 Systems of Linear Equations - 9.1 Exercises - Page 857: 27

Answer

$$\left\{ {\left( {4,6} \right)} \right\}$$

Work Step by Step

$$\eqalign{ & \frac{x}{2} + \,\,\,\,\,\,\,\frac{y}{3}\, = 4\,\,\,\,\, \cr & \frac{{3x}}{2} + \frac{{3y}}{2} = 15\,\, \cr & {\text{Clear the denominators}} \cr & 6\left( {\frac{x}{2}} \right) + \,\,\,\,\,\,\,6\left( {\frac{y}{3}\,} \right) = 6\left( 4 \right)\,\,\,\,\, \cr & 2\left( {\frac{{3x}}{2}} \right) + \,\,\,2\left( {\frac{{3y}}{2}} \right) = 2\left( {15} \right)\,\, \cr & \cr & 3x + \,\,\,2y = 24\,\,\,\,\,\left( {\bf{1}} \right) \cr & 3x + \,\,\,3y = 30\,\,\left( {\bf{2}} \right) \cr & {\text{Multiply the equation }}\left( {\bf{1}} \right){\text{ by }} - 1{\text{ }} \cr & - 3x - \,2y = - 24\,\,\,\, \cr & \,\,3x + \,\,\,3y = 30\,\, \cr & {\text{Add both equations}} \cr & - 3x - \,2y = - 24\,\,\,\, \cr & \,\,3x + \,\,\,3y = 30\,\, \cr & - - - - - - - - - - - \cr & 0x\,\,\,\,\, + y\,\,\, = 6 \cr & y = 6 \cr & {\text{Substitute }}y = 6{\text{ into the equation }}\left( {\bf{1}} \right) \cr & 3x + \,\,\,2\left( 6 \right) = 24 \cr & 3x + \,\,12 = 24 \cr & 3x = \,\,12 \cr & x = 4 \cr & \cr & {\text{The solution set is}} \cr & \left\{ {\left( {4,6} \right)} \right\} \cr} $$
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