3x/2-5y/3=-2. ,X/3+y/2=13/6

1.	3x/2-5y/3=-2. ,X/3+y/2=13/6
Answer» The given system of equations may be written as{tex}9x -10y + 12 = 0{/tex} ...(i){tex}2x + 3y - 13 = 0{/tex}.... (ii)From (ii), we get\xa0{tex} y = \\frac { 13 - 2 x } { 3 }{/tex}Substituting\xa0{tex} y = \\frac { 13 - 2 x } { 3 }{/tex}\xa0in (i), we get{tex} 9 x - \\frac { 10 ( 13 - 2 x ) } { 3 } + 12 = 0{/tex}{tex} \\Rightarrow{/tex}\xa0{tex}27x - 10(13 - 2x) + 36 = 0{/tex}{tex} \\Rightarrow{/tex}\xa0{tex}27x -130 + 20x + 36 = 0{/tex}{tex} \\Rightarrow{/tex}\xa0{tex}47x - 94 = 0{/tex}{tex} \\Rightarrow{/tex}\xa0{tex}47x = 94{/tex}{tex} \\Rightarrow x = \\frac { 94 } { 47 } = 2{/tex}Substituting {tex}x = 2{/tex} in (i), we get9\xa0{tex} \\times{/tex} 2 - 10y + 12 = 0\xa0{tex} \\Rightarrow 10 y = 30 {/tex}{tex}\\Rightarrow y = \\frac { 30 } { 10 } = 3{/tex}Hence, x = 2 and y = 3 is the required solution.

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