We have 21xç ÷ ç ÷ è = 13 (1) - 41y51xç ÷ ç ÷ è ø = -2 (2)If we substitute 1x = p and 1y = q, we get the following pair of linear equations: 2p + 3q = 13 (3)5p - 4q = -2 (4)Coefficients of q are 3 and 4 and their LCM is 12. Using the elimination method :Equation (3) × 4 8p + 12q = 52 Equation (4) × 3 15p - 12q = -6 'q' terms have opposite sign, so we add the two equations. 23p= 46p = 4623 = 2Substitute the value of p in equation (3)2(2) +3q = 133q = 13 - 4 = 9q = 93 = 3But,1x = p = 2 Þ x = 121y = q = 3 Þ y = 13 Example-13. Kavitha thought of constructing 2 more rooms in her house. She enquired aboutthe labour. She came to know that 6 men and 8 women could finish this work in 14 days. But shewishes to complete that work in only 10 days. When she enquired, she was told that 8 men and12 women could finish the work in 10 days. Find out how much time would be taken to finish thework if one man or one woman worked alone. Solution : Let the time taken by one man to finish the work = x days.