Question

Solve : ax +by=a-b bx-ay=a+b find the value of x and y

Answer 1

ax+by=a-b

Multiply this equation to b

abx+b^2(y)=ab-b^2

bx-ay=a+b

Multiply it by a

abx-a^2(y)=a^2+ab

Solve both equations

Subtract it

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

y=-1

Second equation

bx-ay=a+b

Put value of y

bx+a=a+b

bx=b

x=1

So y=-1 and x=1