Question

Solve for x and y: mx-ny=m2+n2;x-y=2m

Answer 1

mx - ny = m² + n²
x - y = 2n

From second equation,
x-y=2n
⇒ x = 2n + y

Putting in first equation,
m(2n+y) – ny = m² + n²
⇒ 2mn + (m-n)y = m² + n² 
⇒ (m-n)y = m² + n² – 2mn
⇒ (m-n)y = (m-n)²
⇒ y = (m-n)² / (m-n) 
⇒ y = m - n

x = 2n+ y = 2n + m – n
⇒ x = m + n

Answer 2

Concept:

Time interval is the time period between any two time instances. Time gives us the existence of an event in past or in future.

Given:

The equation $mx-ny=m2+n2;x-y=2m$

Find:

Solve for $x,y$.

Solution:

According to the problem,

The first equation,

$mx-ny=m^2+n^2$

$x-y=2n.....(i)$

The second equation,

$x-y=2n$

$x=2n+y.....(ii)$

Putting value of $x$ in $(i)$ we get,

$m(2n+y)-ny=m^2+n^2$

$2mn+(m-n)y=m^2+n^2$

$(m-n)y=(m-n)^{2}$

$y=\frac{(m-n)^2}{(m-n)}$

$y=m-n$

Now putting the value of $y$ in $(ii)$ we get,

$x=2n+(m-n)$

$x=m+n$

Hence, the value of $x=m+n$ and $y=m-n$