Question

solve the following pair of linear equation by substitution method

1. x + y = a - b
ax - by = a² + b²

Answer 1

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HERE IS YOUR ANSWER ☞
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$given \: equation \: = > \\ \\ = > x + y = a - b \: \: \: ..........eq _{1} \\ \\ = > \: ax - by \: = \: {a}^{2} + {b}^{2} \\ \\ = > x = a - b - y \: \: \: \: .....(by \: eq _{1}) \\ \\ plug \: the \: value \: of \: x \: in \: eq _{2} \: we \: get \\ \\ = > a(a - b - y) - by = {a}^{2} + {b}^{2} \\ \\ = > {a}^{2} - ab - ay - by = {a}^{2} + {b}^{2} \\ \\ = > \: - y(a + b) = {b}^{2} + ab \\ \\ = > y = \frac{ - b(a + b)}{(a + b)} \\ \\ = > \: y = - b \: \: \: \: \: ........answer \\ \\ now \: \\ \\ plug \: the \: value \: of \: y \: in \: eq _{1} \: we \: get \\ \\ = > x + y = a - b \\ \\ = > x + ( - b) = a - b \\ \\ = > x - b = a - b \\ \\ = > \: x \: = \: a \: \: \: \: \: \: \: .......answer$


hence, your answer is :-

{ X = a and Y = -b }

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