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| 1. |
Find value of a and b for infinitely many solution 2x -3y = 7 (a+b) x -(a+b-3) y =4a+b |
| Answer» Here\xa0{tex}{a_1} = 2,{b_1} = - 3,{c_1} = 7{/tex}\xa0and\xa0{tex}{a_2} = a + b,{b_2} = - \\left( {a + b - 3} \\right),{c_2} = 4a + b{/tex}For infinitely many solutions,\xa0{tex}{{{a_1}} \\over {{a_2}}} = {{{b_1}} \\over {{b_2}}} = {{{c_1}} \\over {{c_2}}}{/tex}=> {tex}{2 \\over {a + b}} = {{ - 3} \\over { - a - b + 3}} = {7 \\over {4a + b}}{/tex}Taking\xa0{tex}{2 \\over {a + b}} = {{ - 3} \\over { - a - b + 3}}{/tex}=> {tex} - 2a - 2b + 6 = - 3a - 3b{/tex}=> {tex}a - b = 6{/tex} .........(i)Again taking\xa0{tex}{2 \\over {a + b}} = {7 \\over {4a + b}}{/tex}=> {tex}8a + 2b = 7a + 7b{/tex}=> {tex}a - 5b = 0{/tex} ..............(ii)On solving eq.(i) and (ii){tex}a = {{15} \\over 2},b = {3 \\over 2}{/tex} | |