InterviewSolution
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InterviewSolution
| 1. |
1/2x+1/3y=2,1/3x+1/2y=13/6 |
| Answer» {tex}{\\frac{1}{{2x}} + \\frac{1}{{3y}} = 2}{/tex} ... (1){tex}\\frac{1}{{3x}} + \\frac{1}{{2y}} = \\frac{{13}}{6}{/tex} ...(2)Let {tex}\\frac{1}{x}{/tex}= p and {tex}\\frac{1}{y}{/tex}= qPutting this in equation (1) and (2), we get{tex}\\frac{p}{2} + \\frac{q}{3} = 2{/tex}\xa0and\xa0{tex}\\;\\frac{p}{3} + \\frac{q}{2} = \\frac{{13}}{6}{/tex}{tex}\\Rightarrow{/tex}\xa03p + 2q = 12 and 6(2p +3q) = 13 (6){tex}\\Rightarrow{/tex}\xa03p + 2q = 12 and 2p + 3q = 13{tex}\\Rightarrow{/tex}\xa03p + 2q - 12 = 0 .................. (3) and2p + 3q - 13 = 0 ................. (4){tex}\\frac{p}{{2( - 13) - 3( - 12)}} = \\frac{q}{{( - 12)2 - ( - 13)3}}{/tex}{tex} = \\frac{1}{{3 \\times 3 - 2 \\times 2}}{/tex}{tex}\\Rightarrow \\frac{p}{{ - 26 + 36}} = \\frac{q}{{ - 24 + 39}} = \\frac{1}{{9 - 4}}{/tex}{tex} \\Rightarrow \\frac{p}{{10}} = \\frac{q}{{15}} = \\frac{1}{5} \\Rightarrow \\frac{p}{{10}} = \\frac{1}{5}\\,{\\text{and}}\\,\\frac{q}{{15}} = \\frac{1}{5}{/tex}{tex}\\Rightarrow{/tex}\xa0p = 2 and q = 3But {tex}\\frac{1}{x}{/tex}\xa0= p and {tex}\\frac{1}{y}{/tex}\xa0= qPutting value of p and q in this we get,x = {tex}\\frac{1}{2}{/tex}and y = {tex}\\frac{1}{2}{/tex} | |