Question

Solve: ax + by = a - b and bx - ay = a + b Please send the photo of it​

Answer 1

Step-by-step explanation:

$\huge\underline\mathcal{\red{Question:-}}$

$\implies$Solve: ax + by = a - b and bx - ay = a + b

Taking the LCM of the Left Hand Side we have;

$\frac{ab - {b}^{2} - {b}^{2}y - {a}^{2} y }{a} = a + b$

Moving a to the RHS we have;

$ab - {b}^{2} - {b}^{2} y - {a}^{2} y = a(a + b)$

$ab - {b }^{2} - {b}^{2} y - {a}^{2} y = {a}^{2} + ab$

$- {b}^{2} - {b}^{2} y - {a}^{2} y = {a}^{2} + ab - ab$

$- {b}^{2} - {b}^{2} y - {a}^{2} y = {a}^{2}$

Moving ${-b}^{2}$ to the RHS and taking y common in the LHS we have;

$- y( {b}^{2} + {a}^{2} ) = {a}^{2} + {b}^{2}$

$- y = 1$

y = -1

Now,

Putting the value of y in (3) We have;

$x = \frac{a - b - b( - 1)}{a}$

$x = \frac{a - b + b}{a}$

$x = \frac{a}{a}$

x = 1