Chapter 9 - Systems and Matrices - 9.1 Systems of Linear Equations - 9.1 Exercises - Page 857: 29

$$\left\{ {\left( {5,2} \right)} \right\}$$

$$\eqalign{ & \frac{{2x - 1}}{3} + \,\,\frac{{y + 2}}{4}\, = 4\,\,\,\left( {\bf{1}} \right) \cr & \,\,\frac{{x + 3}}{2} - \,\frac{{x - y}}{3}\, = 3\,\,\,\left( {\bf{2}} \right) \cr & {\text{Clear the denominators}} \cr & 12\left( {\frac{{2x - 1}}{3}} \right) + \,\,12\left( {\frac{{y + 2}}{4}} \right)\, = 12\left( 4 \right)\,\, \cr & \,6\,\left( {\frac{{x + 3}}{2}} \right) - \,6\left( {\frac{{x - y}}{3}} \right)\, = 6\left( 3 \right)\,\,\,\,\,\, \cr & \cr & \,\,\,\,4\left( {2x - 1} \right) + \,\,3\left( {y + 2} \right) = 48\,\,\, \cr & \,3\left( {x + 3} \right)\,\,\,\,\,\, - 2\left( {x - y} \right) = 18\,\,\,\,\,\,\, \cr & \cr & 8x - 4\,\,\,\, + \,3y\,\, + 6 = 48\,\,\, \cr & 3x + 9\, - 2x + 2y = 18\,\,\,\, \cr & \cr & 8x + \,3y = 46\,\,\,\left( {\bf{1}} \right) \cr & x + 2y = 9\,\,\,\,\,\,\,\left( {\bf{2}} \right) \cr & \cr & {\text{Multiply the equation }}\left( {\bf{2}} \right){\text{ by }} - 8 \cr & \,\,\,\,\,\,8x + \,3y = 46\,\, \cr & - 8x - 16y = - 72\,\,\,\, \cr & {\text{Add both equations}} \cr & \,\,\,\,\,\,8x + \,3y = 46\,\, \cr & - 8x - 16y = - 72\,\,\,\, \cr & - - - - - - - - - - - \cr & 0x - 13y\,\,\,\,\,\,\,\, = - 26 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,y = 2 \cr & {\text{Substitute }}y = 2{\text{ into the equation }}\left( {\bf{2}} \right) \cr & x + 2\left( 2 \right) = 9\, \cr & x = 5 \cr & \cr & {\text{The solution set is}} \cr & \left\{ {\left( {5,2} \right)} \right\} \cr} $$