Question

solve the following: (a+c)x - (a-c)y = 2ab ; (a+b)x -(a-b)x = 2ab​

Answer 1

(a+c)x − (a−c)y = 2ab ....(1)

(a+b)x − (a−b)y = 2ab ..(2)

Adding (1) and (2), we get,

(a+c+a+b)x − (a−c+a−b)y = 4ab

⇒(2a+b+c)x − (2a−b−c)y = 4ab

⇒(2a+b+c)x + (b+c−2a)y = 4ab ...(3)

Subtracting (2) from (1), we get

(c−b)x + (c−b)y = 0

⇒(c−b)(x+y) = 0

⇒x + y = 0

⇒y = − x ...(4)

putting the value of y in (3), we get

(2a+b+c)x + (b+c−2a)(−x) = 4ab

⇒[(2a+b+c) −(b+c−2a)]x = 4ab

⇒(2a+b+c−b−c+2a)x = 4ab

⇒4ax = 4ab

⇒x = b

Now, from (4), we get

y = −b

so, x = b and y = − b is the solution.