Question

ax + by = 7 and bx + ay = 13 then (a + b)(x + y) + (a - b)(x - y) is equal to :​

Answer 1

SOLUTION

GIVEN

ax + by = 7 and bx + ay = 13

TO DETERMINE

The value of

(a + b)(x + y) + (a - b)(x - y)

EVALUATION

Here it is given that

ax + by = 7 - - - - (1)

bx + ay = 13 - - - - - - (2)

Adding Equation 1 and Equation 2 we get

(a + b)x + (a + b)y = 20 - - - - - (3)

Subtracting Equation 2 from Equation 1 we get

ax + by - bx - ay = 7 - 13

⇒ (a - b)x - (a - b)y = - 6 - - - - - (4)

Now

(a + b)(x + y) + (a - b)(x - y)

= 20 - 6

= 14

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