Question

solve the following system of equations by elimination method x+y=a-b
ax-by=a²+b² ​

Answer 1

☆ Question :-

Solve the following system of equations by elimination method :-

$\sf \: x+y=a-b$

$\sf \: ax-by=a²+b²$

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☆ Required Answer:-

$\sf \: ⟼x = a$

$\sf \: ⟼y = - \: b$

☆ Explanation :-

$\sf \: x+y=a-b \: ⟼ \: (1)$

$\sf \: ax-by=a²+b² \: ⟼ \: (2)$

Multiply equation (1) by b, we get

$\sf \: \: bx + by = ab \: - {b}^{2} ⟼ \: (3)$

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

On Adding equation (2) and (3), we get

$\sf \: ⟼ax \: + \: bx \: = {a}^{2} + ab$

$\sf \: ⟼ \: x(a + b) = a(a + b)$

$\sf \: ⟼ \: x = a \: \sf \: ⟼ \: (4)$

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

On substituting the value of x in equation (1), we get

$\sf \: ⟼ \: a \: + \: y = a \: - \: b$

$\sf \: ⟼ \: y \: = \: - \: b \: \sf \: ⟼ \: (5)$

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

$\large{\boxed{\boxed{\tt{{x = \: a}}}}}$

$\large{\boxed{\boxed{\tt{{y \: = \: - \: b}}}}}$

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