Solve for x and y : 6x + 3y = 7xy, 3x + 9y = 11xy.

1.	Solve for x and y : 6x + 3y = 7xy, 3x + 9y = 11xy.
Answer» The given equations are as follows: 6x + 3y = 7xy ………….(i)3x + 9y = 11xy …………(ii)For equation (i), we have: 6x+3y/ xy = 7 On dividing each of the given equations by xy, we get{tex}\\frac { 6 } { y } + \\frac { 3 } { x } = 7{/tex}.......(i){tex}\\frac { 3 } { y } + \\frac { 9 } { x } = 11{/tex}.....(ii)Putting {tex}\\frac 1x{/tex}\xa0= u and {tex}\\frac 1y{/tex}\xa0= v\xa0in (i) and (ii), we get{tex}6v + 3u\xa0= 7{/tex}..... (iii){tex}3v\xa0+ 9u\xa0= 11{/tex}.. ..(iv)Multiplying (iii) by 3 and subtracting (iv) from the result, we get{tex}18v - 3v = 21 - 11{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}15v = 10{/tex}{tex}\\Rightarrow \\quad v = \\frac { 10 } { 15 } = \\frac { 2 } { 3 }{/tex}Putting v\xa0=\xa0{tex}\\frac 23{/tex}\xa0in (iii), we get{tex}\\left( 6 \\times \\frac { 2 } { 3 } \\right) + 3 u = 7{/tex}{tex}\\Rightarrow 4 + 3 u = 7 \\Rightarrow 3 u = 3 \\Rightarrow u = 1{/tex}{tex}u = 1{/tex}\xa0{tex}\\Rightarrow \\frac { 1 } { x } = 1 \\Rightarrow x = 1{/tex}{tex}v = \\frac { 2 } { 3 } \\Rightarrow \\frac { 1 } { y } = \\frac { 2 } { 3 }{/tex}{tex}\\Rightarrow 2 y = 3 \\Rightarrow y = \\frac { 3 } { 2 }{/tex}{tex}\\therefore{/tex}{tex}x = 1\\ and\\ y =\xa0{/tex}{tex}\\frac 32{/tex}

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