Question

x+y=a+b , ax-by=a²-b²​

Answer 1

Method Going to use: Cross Multiplication

→ x + y + (- a - b) = 0

→ ax - by + (- a² + b²) = 0

Solution

$\mathsf{\frac{x}{b_1c_2 - c_1 b_2} = \frac{-y}{a_1c_2 - c_1a_2} = \frac{1}{a_1b_2 - b_1a_2}}$

→ x/{1(- a² + b²) - (- a - b)(- b)}

→ x/(- a² + b² - ab - b²)

→ x/{- a(a + b)}

→ - y/{1(- a² + b²) - (- a - b)(a)}

→ - y/(- a² + b² + a² + ab)

→ - y/{b(a + b)}

→ 1/{1(- b) - 1(a)}

→ 1/{-(a + b)}

→ x/{- a(a + b)} = 1/{-(a + b)}

→ x = a

→ - y/{b(a + b)} = 1/{-(a + b)}

→ y = b

Answer 2

Question :-- Solve x+y = a+b, and ax-by = a² - b² ..

Solution :--

Let,

→ x+y = a+b -------------- Equation (1)

→ ax-by = a² - b² ---------- Equation (2)

Multiplying Equation (1) both sides by b , we get,

→ b(x+y) = b(a+b)

→ bx + by = ab + b² --------- Equation (3) .

Now, Adding Equation (2) and Equation (3) we get,

bx + by = ab + b²

ax - by = a² - b²

x(a+b) = ab + a²

→ x(a+b) = a(b+a)

(a+b) will be cancel From both sides ,

→ x = a

Putting this value in Equation (1) now, we get,

→ a + y = a + b

→ y = a - a + b

→ y = b

So, we can say that, x is Equal to a , and y is Equal to b.