Question

solve for x and y using subsitution method : ax/b -by/a =a+b ; ax - by =2ab

Answer 1

Hi...☺

Here is your answer...✌

Given equations :

$\frac{a}{b} x - \frac{b}{a} y = a + b \: \: \: \: \: \: \: \: \: .....(1)\\ \\ and \\ \\ ax - by = 2ab \\ \\ ax = 2ab + by \\ \\ x = \frac{2ab + by}{a} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: .....(2)$

Putting value of x in eq (1)
we get,

$\frac{a}{b} ( \frac{2ab + by}{a} ) - \frac{b}{a} y = a + b \\ \\ \frac{b(2a + y)}{b} - \frac{b}{a} y = a + b \\ \\ 2a + y - \frac{by}{a} = a + b \\ \\ y(1 - \frac{b}{a} ) = a + b - 2a \\ \\ y (\frac{a - b}{a} ) = - a + b \\ \\ y ( \frac{a - b}{a} ) = - (a - b) \\ \\ y = \frac{ - a(a - b)}{(a - b)} \\ \\ \implies y = - a$

Putting y = -a in eq (2)
we get,

$x = \frac{2ab -ab }{a} \\ \\ x = \frac{ab}{a} \\ \\ \implies x = b$

HENCE,

x = b and y = -a