(a+ b)x+(a-b)y=a^2+b^2 (a-b)x+(a+b)y=a^2 + b^2

1.	(a+ b)x+(a-b)y=a^2+b^2 (a-b)x+(a+b)y=a^2 + b^2
Answer» The given system of linear equation is(a – b)x + (a + b)y = a2 – 2ab – b2 ....(1)(a + b)(x + y) = a2 + b2 ....(2)Equation (2) can be written as(a + b)x + (a + b)y = a2 + b2 ....(3)Subtracting equation (3) from equation (1), we get– 2bx = – 2ab – 2b2{tex}\\Rightarrow{/tex} – 2bx = – 2b(a + b){tex}\\Rightarrow{/tex} x = a + bSubstituting this value of x in equation (1), we get(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}Verification: Substituting x = a + b, {tex}y = - \\frac{{2ab}}{{a + b}}{/tex},We find that both the equations (1) and (2) are satisfied as shown below:(a – b)x + (a + b)y = (a – b)(a + b) + (a + b) {tex}\\left\\{ { - \\frac{{2ab}}{{a + b}}} \\right\\}{/tex}= a2 – 2ab – b2(a + b)(x + y) = (a + b){tex}\\left\\{ {(a + b) + (- \\frac{{2ab}}{{a + b}})} \\right\\}{/tex}= (a + b)2 – 2ab= a2 + b2hence, the solution we have got is correct.

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