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By elimination method 3x-y+7/11+2=102y+x+11/7=10 |
| Answer» The given system of equations is{tex}3x - \\frac{{y + 7}}{{11}} + 2 = 10{/tex}\xa0...(i){tex}2y + \\frac{{x - 11}}{7} = 10{/tex}\xa0....(ii)From (i), we get{tex}\\frac{{33x - y - 7 + 22}}{{11}} = 10{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}33x - y + 15 = 10 × 11{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}33x + 15 - 110 = y{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}y = 33x - 95{/tex}From (ii), we get{tex}\\frac{{14y + x + 11}}{7} = 10{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}14y + x + 11 = 10 × 7{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}14y + x + 11 = 70{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}14y + x = 70 - 11{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}14y + x = 59{/tex} ....(iii)Substituting y = 33x - 95 in (iii), we get14(33x - 95) + x = 59{tex}\\Rightarrow{/tex}\xa0462x - 1330 + x = 59{tex}\\Rightarrow{/tex}\xa0463x = 59 + 1330{tex}\\Rightarrow{/tex}\xa0463x = 1389{tex}\\Rightarrow x = \\frac{{1389}}{{463}} = 3{/tex}Putting x = 3, in y = 33x - 95, we gety = 33 {tex}\\times{/tex}\xa03 - 95{tex}\\Rightarrow{/tex}\xa0y = 99 - 95 = 4{tex}\\Rightarrow{/tex} y = 4Hence, Solution of the given system of equation is x = 3, y = 4. | |