Question

Mx-ny=m^2+n^2
X+y=2m

Answer 1

we will apply elimination

Mx-ny=m^2+n^2 .....(1)

X+y=2m ......(2)

multiplying n in eq (2)

Mx-ny=m^2+n^2

nx+ny=2mn

adding both the eq

mx+nx=m^2+n^2+2mn

[a^2+2ab+b^2=(a+b)^2]

x(m+n)=(m+n)^2

x=m+n

putting eq 3 in 2

m+n+y=2m

y=m-n

Thierfore

answer=> x=m+n

=>y=m-n

hope its help you

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Answer 2

Answer:

⇒ $x = m+n$

⇒ $y = m - n$

Step-by-step explanation:

Given :

Solve for x & y if,

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

$x+y=2m$

Solution :

$mx-ny=m^2+n^2$ ...(i)

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

By multiplying (ii) by n,

We get,

⇒ $n(x+y)=2mn$

⇒ $nx+ny=2mn$ ...(iii)

By adding (i) & (iii),

We get,

⇒ $(mx - ny) + (nx + ny) = m^2 + n^2 + 2mn$

⇒ $(m + n)x = (m + n)^2$

⇒ $x = \frac{(m+n)^2}{m+n} = m+n$

By substituting value of x, in (ii),

We get,

⇒ $x + y = 2m$

⇒ $(m + n) + y = 2m$

⇒ $y = 2m - m - n$

⇒ $y = m - n$

∴ $x = m+n$

∴ $y = m - n$