Question

What will be the solution of these equations ax+by = a-b and bx- ay =a+b?

Answer 1

The given equations are;

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

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

Then,. b×eq(1)=abx+b×by=ab-bb

a×eq(2)=abx-a×ay=aa-ab

(-). (+). (-) (+).

a2y+b2y=(-aa-bb)

(a2+b2)y=-(aa+bb)

y= -(aa-bb)÷(aa+bb)

y= (-1)

Put the value of y in equations.....(1)

ax+b×(-1)=a-b

ax-b=a-b

ax=a

X=1

Then, The answer is (X,y)= {1,(-1)}