Question

ax-by=a2+b2, x+y=2a solve by cross multiplication method​

Answer 1

Answer:

Solution is

x=a+b

y=a-b

Step-by-step explanation:

Given equations are

$ax-by-(a^2+b^2)=0$

$x+y-2a=0$

By cross multiplication rule,

$\frac{x}{2ab+(a^2+b^2)}=\frac{y}{-(a^2+b^2)+2a^2}=\frac{1}{a+b}$

$\implies\:\frac{x}{2ab+(a^2+b^2)}=\frac{1}{a+b}$

$\implies\:\frac{x}{(a+b)^2}=\frac{1}{a+b}$

$\implies\:x=\frac{(a+b)^2}{a+b}$

$\implies\:x=a+b$

Also,

$\frac{y}{-(a^2+b^2)+2a^2}=\frac{1}{a+b}$

$\implies\:\frac{y}{-a^2-b^2+2a^2}=\frac{1}{a+b}$

$\implies\:\frac{y}{a^2-b^2}=\frac{1}{a+b}$

$\implies\:\frac{y}{(a+b)(a-b)}=\frac{1}{a+b}$

$\implies\:y=a-b$

Answer 2

Solution is

x=a+b

y=a-b

Step-by-step explanation:

Given equations are

ax-by-(a^2+b^2)=0ax−by−(a

2

+b

2

)=0

x+y-2a=0x+y−2a=0

By cross multiplication rule,

\frac{x}{2ab+(a^2+b^2)}=\frac{y}{-(a^2+b^2)+2a^2}=\frac{1}{a+b}

2ab+(a

2

+b

2

)

x

=

−(a

2

+b

2

)+2a

2

y

=

a+b

1

\implies\:\frac{x}{2ab+(a^2+b^2)}=\frac{1}{a+b}⟹

2ab+(a

2

+b

2

)

x

=

a+b

1

\implies\:\frac{x}{(a+b)^2}=\frac{1}{a+b}⟹

(a+b)

2

x

=

a+b

1

\implies\:x=\frac{(a+b)^2}{a+b}⟹x=

a+b

(a+b)

2

\implies\:x=a+b⟹x=a+b

Also,

\frac{y}{-(a^2+b^2)+2a^2}=\frac{1}{a+b}

−(a

2

+b

2

)+2a

2

y

=

a+b

1

\implies\:\frac{y}{-a^2-b^2+2a^2}=\frac{1}{a+b}⟹

−a

2

−b

2

+2a

2

y

=

a+b

1

\implies\:\frac{y}{a^2-b^2}=\frac{1}{a+b}⟹

a

2

−b

2

y

=

a+b

1

\implies\:\frac{y}{(a+b)(a-b)}=\frac{1}{a+b}⟹

(a+b)(a−b)

y

=

a+b

1

\implies\:y=a-b⟹y=a−b