Question

9. mx-ny=m2 + n
x+y = 2m
CBSE 2006)
Solve each of the following system of equations by method of elimination :​

Answer 1

☆ Correct Question :-

Solve each of the following system of equations by method of elimination :

$\sf \: mx - ny = {m}^{2} + {n}^{2}$

$\sf \: x + y = 2m$

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$\bf \:☆Required \: Answer:-$

$\sf \: ⟼x \: = m + n \\ \sf \: ⟼y = m - n$

$\bf \: ☆ \: Explanation:-$

$\sf \: mx - ny = {m}^{2} + {n}^{2} \: \sf \: ⟼ \: (1)$

$\sf \: x + y = 2m \: ⟼ \: (2)$

Multiply equation (2) by n, we get

$\sf \: nx + ny = 2mn \: ⟼ \: (3)$

$\begin{gathered}\bf\red{So,}\end{gathered}$

On Adding equation (1) and (3), we get

$\sf \: ⟼ \: mx + nx = {m}^{2} + {n}^{2} + 2mn$

$\sf \: ⟼x(m + n) = {(m + n)}^{2}$

$\sf \: ⟼ \: x = m + n \: \sf \: ⟼ \: (4)$

$\begin{gathered}\bf\red{Now,}\end{gathered}$

On Substituting value of x in equation (2), we get

$\sf \: ⟼m + n + y = 2m$

$\sf \: ⟼y = 2m - m - n$

$\sf \: ⟼y = m \: - n \: \sf \: ⟼ \: (5)$

$\begin{gathered}\bf\blue{Hence}\end{gathered}$

$\large{\boxed{\boxed{\tt{{x = m \: + \: n}}}}}$

$\large{\boxed{\boxed{\tt{{y = m \: - \: n}}}}}$

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