Question

If 99x + 101y = 499 and 101x + 99y = 501 then the value of x
square
+ y square
is

options
a)5 b)13 c)25 d)100​

Answer 1

❍ Given :-

→ 99x + 101y = 499 •••• Equation ①

→ 101x + 99y = 501 •••• Equation ②

❍ To Find :-

• Value of x and y

❍ Solution :-

➸ Adding ① and ②,

⇒ 99x + 101y + (101x + 99y) = 499 + 501

⇒ 200x + 200y = 1000

➸ Dividing equation by 200,

∴ x + y = 5 •••• Equation ③

➸ Subtracting ① from ②,

⇒ 101x + 99y - (99x + 101y) = 501 - 499

⇒ 2x - 2y = 2

➸ Dividing equation by 2,

→ x - y = 1 •••• Equation ④

➸ Adding ③ and ④,

⇒ x + y + (x - y) = 5 + 1

⇒ 2x = 6

⇒ $\frac{\cancel 6}{\cancel 2}$

⇒ $\fbox{x = 3}$

➸ Putting x = 3 in equation ④,

⇒ x - y = 1

⇒ 3 - y = 1

⇒ -y = -2

⇒ $\fbox{y = 2}$

Therefore, x = 3 and y = 2.

Now, we have to find x² + y²,

→ (3)² + (2)²

→ 9 + 4

→ 13

Hence, x² + y² is equal to 13.

Option (B) 13 is right option.