Question

Solve : mx-ny=m2 + n2 ; x+y = 2m by cross multiplication

Answer 1

given

mx-ny=m^2+n^2-------(1)

x+y=2m--------(2)

multiplying eq(1) by coefficient of x i.e.1 and eq(2) by coefficient of x i.e. m

we get,

mx-ny=m^2+n^2-------(3)

mx+my=2m^2----------(4)

subtracting eq(3) and (4) we get

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

or -y(m+n)=-m^2+n^2

               =-(m+n)(m-n)/(m+n)

              y = m-n-----(5)

by putting the value of y in eq.(2) we get,

x=2m-(m-n)

hence solution is , x=m+n &y=m-n

Answer 2

Answer:

The value of $x=m+n$ and $y = m-n$

Step-by-step explanation:

• The equation we have is
  $mx+ny=m^2 +n^2\\x+y=2m$
• Now when we bring the RHs to LHS we get
  $\frac{mx+ny}{m^2 + n^2} = 1$ and $\frac{x+y}{2m}=1$
• Now by equalizing them we get
  $\frac{mx+ny}{m^2 + n^2} = 1 = \frac{x+y}{2m}$
• By cross multiplying them we get
  $(mx-ny) * 2m = (x+y )(m^2 + n^2)$
  $2m^2x -2mny = m^2x+n^2x+m^2y+n^2y$
• From solving this equation we get
  $x=m+n$ and $y = m-n$
  #SPJ2