Question

solve the following pair of linear equation X + Y = a + b and ax - b = a ^2 - b^2​

Answer 1

X = a

Y = b

Step-by-step explanation:

x+y−(a+b)=0

ax−by−(a² - b²)=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