MathematicsChoose the correct answer from the alternatives given. If x+y-82=x+2y-143=3x+y-1211 then find the values of x and y, respectively.

Choose the correct answer from the alternatives given. If $\frac{x + y - 8}{2} = \frac{x + 2 y - 14}{3} = \frac{3 x + y - 12}{11}$ then find the values of x and y, respectively.

Given that

\frac{x + y - 8}{2} = \frac{x + 2 y - 14}{3}

⇒

3 x + 3 y - 24 = 2 x + 4 y - 28

⇒

x - y = - 4

....... (1)
Also given,

\frac{x + y - 8}{2} = \frac{3 x + y - 12}{11}

.
⇒

11 x + 11 y - 88 = 6 x + 2 y - 24

⇒

5 x + 9 y = 64

....... (2)
Multiplying equation (1) by 9.

9 x - 9 y = - 36

… (3)
Adding equations (2) and (3),

14 x = 28

⇒

x = 2

Put value of x in equation (1),

2 - y = - 4

⇒

- y = - 4 - 2

⇒

- y = - 6

⇒

y = 6

We get

x = 2, y = 6

.
Hence, the correct option is 1.

JEE