Question

solve ax+by=a-b and bx-ay=a+b

Answer 1

ax + by  = a-b ------------------------------------------(1)

bx - ay = a+b -------------------------------------------(2)

by multiplying eqn. (1) by a and (2) by b

we get,

a^2*x + aby = a^2 - ab ------------------------------(3)

b^2*x - aby = b^2 + ab ------------------------------(4)

Adding (3) and (4)

(a^2 + b^2)x = a^2 + b^2

Hence, x = 1

Putting x = 1 in (3)

a^2 + aby = a^2 - ab

aby = -ab

y = -1

Thus, solution of above eqns. are x = 1 and y = -1

Answer 2

Step-by-step explanation:

ax + by  = a-b ------------------------------------------(1)

bx - ay = a+b -------------------------------------------(2)

by multiplying eqn. (1) by a and (2) by b

we get,

a^2*x + aby = a^2 - ab ------------------------------(3)

b^2*x - aby = b^2 + ab ------------------------------(4)

Adding (3) and (4)

(a^2 + b^2)x = a^2 + b^2

Hence, x = 1

Putting x = 1 in (3)

a^2 + aby = a^2 - ab

aby = -ab

y = -1

Thus, solution of above eqns. are x = 1 and y = -1