Question

solve by elimination method ;x+y=a-b,ax-by=a^2+b^2.​

Answer 1

ax + by = a - b …….(1)

bx - ay = a + b …….(2)

Now multiply equation 1 with b and equation 2 with a.

ax + by = a - b ……(1) × b

~ abx + b^2y = ab - b^2

bx - ay = a + b …….(2) × a

~ abx - a^2y = a^2 + ab

Subtracting them we get~

a^2y + b^2y = -a^2-b^2

~ y(a^2 + b^2) = -(a^2 + b^2)

~y = -(a^2+b^2)/a^2+b^2

~y = -1

Putting the value of y in equation 1 we get~

ax + by = a-b

~ ax +b×(-1) = a - b

~ ax -b = a- b

~ ax = a-b+ b

~ x = a/a

~ x = 1

Thus, x=1 , y=-1