Question

ax+by=1, bx-ay=a+b find the value of x and y​

Answer 1

Ax+by=a-b

ax=a-b-by

x=a-b-by/a←

bx-ay=a+b

substituting

b(a-b-by/a)-ay=a+b

ab-b²-b²y/a-ay=a+b

ab-b²-b²y-a²y/a=a+b

ab-b²-(b²+a²)y=a²+ab

-(b²+a²)y=a²+ab-ab+b²

(b²+a²)y=-(a²+b²)

y=-(a²+b²)/a²+b²

y=-1←

substituting value of y

x=a-b-b(-1)/a

x=a-b+b/a

x=a/a

x=1

Answer 2

Answer:

:

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

bx+a=a+b

bx=b

x=1

So y=-1 and x=1