Solve pair of linear equation : …
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Sia ? 6 years, 4 months ago
(a - b)x + (a + b)y = a2 - 2ab - b2 ...(1)
(a + b)(x + y) = a2 + b2 {tex}\Rightarrow{/tex} (a + b)x + (a + b)y = a2 + b2 ....(2)
Subtracting equation (2) from (1), we obtain:
(a - b)x - (a + b)x = (a2 - 2ab - b2) - (a2 + b2)
{tex}\Rightarrow{/tex} (a - b - a - b)x = -2ab - 2b2
{tex}\Rightarrow{/tex} -2bx = -2b(a + b)
{tex}\Rightarrow{/tex} x = a + b
Substituting the value of x in equation (1), we obtain:
(a - b) (a + b) + (a + b)y = a2 - 2ab - b2
{tex}\Rightarrow{/tex} a2 - b2 + (a + b)y = a2 - 2ab - b2 {tex}\Rightarrow{/tex} (a + b)y = -2ab
{tex}\Rightarrow y = \frac{{ - 2ab}}{{a + b}}{/tex}
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