Question

A x minus b y equal to a square + b square and X + y equal to 2

Answer 1

ANSWER

The given system of equations may be written as

x+y−(a+b)=0

ax−by−(a

2

−b

2

)=0

By cross-multiplication, we get

−(a

2

−b

2

)−(−b)×−(a+b)

x

=

−(a

2

−b

2

)−a×−(a+b)

−y

=

1×−b−a×1

1

⇒

−a

2

+b

2

−ab−b

2

x

=

−a

2

+b

2

+a

2

+ab

−y

=

−b−a

1

⇒

−a(a+b)

x

=

b(a+b)

−y

=

−(a+b)

1

⇒

−a(a+b)

x

=

−b(a+b)

y

=

−(a+b)

1

⇒x=

−(a+b)

−a(a+b)

=a and y=

−(a+b)

−b(a+b)

=b

Hence, the solution of the given system of equations is x=a,y=b.