Question

solve the equation by substitution method

Answer 1

$ax( \frac{a + b - a + b}{ {a}^{2} - {b}^{2} } ) + by( \frac{b + a - b + a}{ {b}^{2} - {a}^{2} } ) = 2 \\ = \frac{2bax}{ {a}^{2} - {b}^{2} } + \frac{2aby}{ {b}^{2} - {a}^{2} } = 2$
$\frac{2abx}{ {a}^{2} - {b}^{2} } - \frac{2aby}{ {a}^{2} - {b}^{2} } = 2 \\ abx - aby = {a}^{2} - {b}^{2}$
now substitute value of x from eq2 into eq2
$x = \frac{(a + b) - ay}{b}$
$ab ( \frac{(a + b) - 2y}{a} ) - aby = {a}^{2} - {b}^{2} \\ ab + {b}^{2} - 2by - aby = {a}^{2} - {b}^{2} \\ - (2b + ab)y = {a}^{2} - {b}^{2} - {b}^{2} - ab \\ y = \frac{ {a}^{2} - 2 {b}^{2} - ab }{ - (2b + ab)}$
put the value of y in eq1