Question

Find solution using elimination method.
ax+by=a-b
bx-ay=a+b​

Answer 1

Answer:

x=1

y=-1

Step-by-step explanation:

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

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

Multiply eq. (i) by a and eq. (ii) by b and then, add eq. (i) and (ii)

a²x+aby+b²x-aby= a²-ab+ab+b²

a²x+b²x=a²+b²

x(a²+b²)= a²+b²

x=1

Putting x=1 in eq.(i)

a(1)+by=a-b

a+by=a-b

by=-b

y=-1

Hope It Helps :)

Answer 2

Answer:

ax+by=a−b (1)

bx−ay=a+b (2)

Multiply equation (1) with a and equation (2) with b ,

a2x+aby=a2−ab (3)

b2x−aby=ab+b2 (4)

Adding (3) and (4), we get,

(a2+b2)x=a2+b2

⇒x=1

Now, from (1),

ax+by=a−b

a+by=a−b

by=−b

y=−1