a/x-b/y=0
ab^2/x+a^2b/y=a^2+b^2
Answers
Answer
Taking
x
1
=u and
y
1
=v, the above system of equations becomes
au−bv+0=0
ab
2
u+a
2
bv−(a
2
−b
2
)=0
By cross-multiplication, we have
−b×−(a
2
+b
2
)−a
2
b×0
u
=
a×−(a
2
+b
2
)−ab
2
×0
−v
=
a×a
2
b−ab
2
×−b
1
⇒
b(a
2
+b
2
)
u
=
−a(a
2
+b
2
)
−v
=
a
3
b+ab
3
1
⇒
b(a
2
+b
2
)
u
=
a(a
2
+b
2
)
v
=
b(a
2
+b
2
)
1
⇒
b(a
2
+b
2
)
u
=
a(a
2
+b
2
)
v
=
ab(a
2
+b
2
)
1
⇒u=
ab(a
2
+b
2
)
b(a
2
+b
2
)
=
a
1
and
v=
ab(a
2
+b
2
)
a(a
2
+b
2
)
=
b
1
Now, u=
a
1
⇒
x
1
=
a
1
⇒x=a and v=
b
1
⇒
y
1
=
b
1
⇒y=b
Hence, the solution of the given system of equation is x=a,y=b.