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| 1. |
x/3 + y/4 =11 5x/6 - y/3=-7 |
| Answer» The given equations are{tex}\\frac { x } { 3 } + \\frac { y } { 4 } = 11{/tex}{tex}\\frac { 5 x } { 6 } - \\frac { y } { 3 } = - 7{/tex}\xa0Now {tex}\\frac { x } { 3 } + \\frac { y } { 4 } = 11{/tex}\xa0{tex}\\Rightarrow{/tex}{tex}\\frac { 4 x + 3 y } { 12 } = 11{/tex}\xa0(by taking LCM){tex}4x + 3y = 132{/tex} ......(i){tex}\\frac { 5 x } { 6 } - \\frac { y } { 3 } = - 7{/tex}{tex}\\frac { 5 x - 2 y } { 6 } = - 7{/tex}(by taking LCM){tex}5x - 2y = -42{/tex}.........(ii)Multiplying (i) by 2 and (ii) by 3, we get{tex}8x + 6y = 264{/tex} ........(iii){tex}15x - 6y = -126{/tex} ........(iv)Adding (iii) from (iv), we get{tex}23x = 138{/tex}\xa0{tex}\\Rightarrow{/tex}\xa0{tex}x = 6{/tex}Substituting x = 6\xa0in (i),we get{tex}4 \\times 6 + 3 y = 132 \\Rightarrow 3 y = 132 - 24{/tex}{tex}3y = 108{/tex}{tex}y = 36{/tex}{tex}\\therefore{/tex}\xa0Solution is {tex}x = 6, y = 36{/tex} | |