1-THE PAIR OF EQUATION 3x+y =81 , 81x-y =3 has (A) no solution (B)the solution x =5/2 y= 5/2 (C) - Maths - Pair of Linear Equations in Two Variables

Question

1-THE PAIR OF EQUATION 3x+y =81 , 81x-y =3
has
(A) no solution (B)the solution x =5/2 y= 5/2
(C) the solution x=2 y=2 (d) the solution x=17/8 y=15/8

Ajanta Trivedi · Accepted Answer

the given equations are

$3^{x + y} = 81 a n d 81^{x - y} = 3 3^{x + y} = 3^{4} .......... (1) a n d (3^{4})^{x - y} = 3 \Rightarrow 3^{4 (x - y)} = 3^{1} ........... (2)$

from eq(1) and eq(2), comparing the exponents:

$x + y = 4......... (1)' 4 (x - y) = 1 \Rightarrow x - y = \frac{1}{4} ............ (2)'$

adding eq(1)' and eq(2)':

$2 x = 4 + \frac{1}{4} 2 x = \frac{17}{4} x = \frac{17}{8}$

subtracting eq(1)' and eq(2)':

$2 y = 4 - \frac{1}{4} 2 y = \frac{15}{4} y = \frac{15}{8}$

thus option (d) is correct.

hope this helps you.

cheers!!

1-THE PAIR OF EQUATION 3x+y =81 , 81x-y =3 has (A) no solution (B)the solution x =5/2 y= 5/2 (C) the solution x=2 y=2 (d) the solution x=17/8 y=15/8