Question

Please solve this question.

Answer 1

multiply first eq by b and second by a
$abx + {b}^{2} y = b \\ abx + {a}^{2} y = \frac{a(a + b)}{ {a}^{2} + {b}^{2} }$
subtract both equation
${b}^{2} y - {a}^{2} y = \frac{a( a + b)}{ {a}^{2} + {b}^{2} } \\ y( {b}^{2} - {a}^{2} ) = \frac{a(a + b)}{ {b}^{2} + {a}^{2} } \\ y = \frac{a(a + b)}{( {b}^{2} + {a}^{2} )( {b}^{2} - {a}^{2}) } \\ y = \frac{a(a + b)}{ {b}^{4} - {a}^{4} } \\ or \\ y = \: \frac{ - a(a + b)}{ {a}^{4} - {b}^{4} } \\ place \: the \: value \: of \: y \: in \: eq \: 1 \\ ax + by = 1 \\ ax + \frac{ab(a + b)}{ {b}^{4} - {a}^{4} } = 1 \\ ax = 1 - \frac{ab(a + b)}{ {b}^{4} - {a}^{4} } \\ x = \frac{ {b}^{4} - {a}^{4} - ab(a + b) }{ a({b}^{4} - {a}^{4} ) }$