x + y - 8 /2 = x+ 2y -14 /8 = 3x+ y - 12 / 11 solve

1.	x + y - 8 /2 = x+ 2y -14 /8 = 3x+ y - 12 / 11 solve
Answer» The given equations are:{tex}\\frac { x + y - 8 } { 2 } = \\frac { x + 2 y - 14 } { 3 } = \\frac { 3 x + y - 12 } { 11 }{/tex}Therefore, we have{tex}\\frac { x + y - 8 } { 2 } = \\frac { 3 x + y - 12 } { 11 }{/tex}By cross multiplication,we get{tex}11x + 11y - 88 = 6x + 2y - 24{/tex}{tex}11x - 6x + 11y -2y = -24 + 88{/tex}{tex}5x + 9y = 64 {/tex}..........(i)\xa0and {tex}\\frac { x + 2 y - 14 } { 3 } = \\frac { 3 x + y - 12 } { 11 }{/tex}By cross multiplication,we get{tex}11x + 22y -154 = 9x + 3y - 36{/tex}{tex}11x - 9x + 22y -3y = -36 + 154{/tex}{tex}2x + 19y = 118{/tex}.........(ii)Multiplying (i) by 19\xa0and (ii) by 9, we get{tex}95x + 171y = 1216{/tex} .......(iii){tex}18x + 171y = 1062{/tex} .......(iv)Subtracting (iv) from\xa0(iii),we get{tex}77 x = 154 \\Rightarrow x = 2{/tex}Substituting x = 2\xa0in (i),we get{tex}5 \\times 2 + 9 y = 64 \\Rightarrow 9 y - 54{/tex}{tex}\\therefore{/tex}\xa0Solution is x = 2, y = 6

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