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| 1. |
solve for x and y ax/b - by/a = a+b and ax-by=2ab |
| Answer» The given equations may be written as{tex}a^2x - b^2y = a^2b + ab^2{/tex} ....... (i){tex}ax - by = 2ab{/tex} ......... (ii)Multiplying (ii) by b and subtracting the result from (i),\xa0{tex}(a^2\xa0- ab)x = a^2b - ab^2{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}(a^2\xa0- ab)x = b(a^2\xa0- ab){/tex}{tex}\\Rightarrow{/tex}{tex}x = b.{/tex}Putting {tex}x = b{/tex} in\xa0(ii), we get{tex}a b - b y = 2 a b {/tex}{tex}\\Rightarrow b y = - a b{/tex}{tex} \\Rightarrow y = \\frac { - a b } { b } = - a{/tex}Hence, x = b and y = -a. | |