Question

solve for x and y (a-b)X + (a + b)Y = a^2-2 a b-b^2 (a + b) (X + Y) =a^2+b^2

Answer 1

$\textbf{Answer}$

$y = \frac{ - 2ab}{a + b}$

$x = a + b$

$\textbf{Step- By-Step Solution}$

$\textbf{Equation(1)}$

$(a - b)x + (a + b)y = {a}^{2} - 2ab - {b}^{2}$

$\textbf{Equation.2}$

$(a + b)(x + y) = {a}^{2} + {b}^{2}$

$= (a + b)x + (a + b)y = {a}^{2} + {b}^{2}$

$\textbf{On , Solving These Equations}$

$\textbf{Step.1 }$
$(a + b)x - (a - b)x = {a}^{2} + {b}^{2} - ( {a}^{2} - 2ab - {b}^{2} )$

$\textbf{Step.2}$

$ax + bx - ax + bx = {a}^{2} + {b}^{2} - {a}^{2} + 2ab + {b}^{2}$

$\textbf{Step.3}$

On cancel same term

$2bx = 2 {b}^{2} + 2ab$

$\textbf{Step4}$

$x = \frac{2 {b}^{2} + 2ab }{2b}$

$\textbf{Step .5}$

$x = \frac{ {b}^{2} + ab }{b}$

$\textbf{Step 6}$

$x = \frac{b(b + a)}{b}$

$\textbf{Step 7}$

$x = b+ a$

$\textbf{Value of Y}$

$\textbf{Step 1}$

put value of X in eq $\textbf{1}$

$(a - b)(b + a) + (a + b)y = {a}^{2} - 2ab$

$\textbf{Step 2}$

${a}^{2} - {b}^{2} + (a + b)y = {a}^{2} - 2ab$

$\textbf{Step 3}$

$(a + b)y = {a}^{2} - 2ab + {b}^{2} - {a}^{2}$

$\textbf{Step 4}$

$(a + b)y = {b}^{2} - 2ab$

$\textbf{Step 5}$

$y = \frac{ {b}^{2} - 2ab }{a + b}$

$\textbf{Hence}$

$\textbf{Value of X }$

$x = a + b$

$\textbf{Value of Y}$

$y = \frac{ - 2ab}{a + b}$

Answer 2

Answer:

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Step-by-step explanation: