By elimination method - x+1/2 + y-1/3=8 and x-1/3 +y+1/2=9

1.	By elimination method - x+1/2 + y-1/3=8 and x-1/3 +y+1/2=9
Answer» The given equations may be written as{tex} \\frac { x + 1 } { 2 } + \\frac { y - 1 } { 3 } = 8 {/tex}⇒ 3(x + 1) + 2 (y - 1) = 48⇒ 3x + 3 + 2y - 2 = 48⇒ 3x + 2y + 1= 48⇒ 3x+2y = 47 ... (i){tex}\\frac { x - 1 } { 3 } + \\frac { y + 1 } { 2 } = 9{/tex}⇒ 2(x -1 ) + 3(y +1) = 54⇒ 2x - 2 + 3y + 3 = 54⇒ 2x + 3y + 1 = 54⇒ 2x + 3y = 53. ... (ii)Multiplying (i) by 2 and (ii) by 3 and subtracting, we get(4\xa0- 9)y = 94-159{tex} \\Rightarrow - 5 y = - 65 {/tex}{tex}\\Rightarrow y = \\frac { - 65 } { - 5 } {/tex}{tex}\\Rightarrow y = 13{/tex}Putting y = 13 in (i), we get3x\xa0+ (2 {tex} \\times{/tex}\xa013) = 47{tex} \\Rightarrow{/tex} 3x + 26 = 47{tex} \\Rightarrow{/tex} 3x = (47 - 26){tex} \\Rightarrow{/tex}3x = 21{tex} \\Rightarrow \\quad x = \\frac { 21 } { 3 } = 7{/tex}So, x = 7Hence, x = 7 and y = 13

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