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| 1. |
solve for x and yax+by=a+b/2and 3x+5y=4 |
| Answer» {tex}a x + b y = \\frac { a + b } { 2 }{/tex}\xa0or 2ax +2by = a + b ...(i)and 3x + 5y = 4 ...(ii)Multiplying eqn. (i) by 5 and (ii) by 2b, and subtracting,x =\xa0{tex}\\frac{5a - 3b}{2(5a - 3b)}{/tex}\xa0=\xa0{tex}\\frac{1}{2}{/tex}Substitute\xa0{tex}x = \\frac { 1 } { 2 }{/tex}\xa0in eqn. (ii), we get{tex}3 \\frac { 1 } { 2 } + 5 y = 4{/tex}\xa0{tex}5 y = 4 - \\frac { 3 } { 2 }{/tex}\xa0{tex}y = \\frac { 5 } { 2 \\times 5 } = \\frac { 1 } { 2 }{/tex}\xa0Hence\xa0{tex}x = \\frac { 1 } { 2 } \\text { and } y = \\frac { 1 } { 2 }{/tex} | |