Question

Solve for X and y

(a-b)X + (a+b)y = a² - 2ab - b² ; (a+b) (X+y) = a²+b²

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Answer 1

Answer:

x = a + b, y = -2ab/a + b

Step-by-step explanation:

Given Equations are:

(i) (a - b)x + (a + b)y = a² - 2ab - b²

(ii) (a + b)(x + y) = a² + b²

(a + b)x + (a + b)y = a² + b²

Subtracting (i) - (ii), we get

⇒ {(a - b)x + (a + b)y} - {(a + b)x + (a + b)y} = {a² - 2ab - b²} - {a² + b²}

⇒ (a - b)x + (a + b)y - (a + b)x - (a + b)y = a² - 2ab - b² - a² - b²

⇒ (a - b)x - (a + b)x = -2ab - 2b²

⇒ ax - bx - ax - bx = -2b(a + b)

⇒ -2bx = -2b(a + b)

⇒ x = a + b

⇒ x = a + b

Substitute x = a + b in (i), we get

⇒ (a - b)x + (a + b)y = a² - 2ab - b²

⇒ (a - b)(a + b) + (a + b)y = a² - 2ab - b²

⇒ (a - b)(a + b) + (a + b)y = a² - 2ab - b²

⇒ (a² - b²) + (a + b)y = a² - 2ab - b²

⇒ (a + b)y = a² - 2ab - b² - (a² - b²)

⇒ (a + b)y = a² - 2ab - b² - a² + b²

⇒ (a + b)y = -2ab

⇒ y = -2ab/a + b.

Hope it helps!

Answer 2

(a-b)x +(a+b)y =a^2 -2ab-b^2 .... eq1

(a+b)(x+y)=a^2+b^2 ................ eq 2

subtract eq1 to eq 2, or either

2bx = 2ab + 2b^2

x = a + b

substitute x = a + b, to eq 1

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

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

y = 2ab/(a+b)