Question

The pair of equations 5^(x+y) = 625 and 7^(x-y) = 343 has

(a) No solution
(b) Infinite solution
(c) Unique solution
(d) x=2 whole 1/8 and y= 1 whole 7/8​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{5^{x+y}=625\;\&\;7^{x-y}=343}$

$\underline{\textbf{To find:}}$

$\textsf{Nature of solution of the given equations}$

$\underline{\textbf{Solution:}}$

$\mathsf{Consider,}$

$\mathsf{5^{x+y}=625\;\;\;\&\;\;\;7^{x-y}=343}$

$\textsf{This can be written as,}$

$\mathsf{5^{x+y}=5^4\;\;\;\&\;\;\;7^{x-y}=7^3}$

$\textsf{Equating powers, we get}$

$\mathsf{x+y=4}$--------(1)

$\mathsf{x-y=3}$--------(2)

$\mathsf{Adding\;(1)\;and\;(2)}$

$\mathsf{2x=7}$

$\boxed{\mathsf{x=\dfrac{7}{2}}}$

$\mathsf{Put\;x=\dfrac{7}{2}\;in\;(1)}$

$\mathsf{\dfrac{7}{2}+y=4}$

$\mathsf{y=4-\dfrac{7}{2}}$

$\boxed{\mathsf{y=\dfrac{1}{2}}}$

$\therefore\textbf{The given equations has unique solution}$

$\underline{\textbf{Answer:}}$

$\mathsf{Option\;(c)\;is\;correct}$

Answer 2

Answer:

(c) unique solution

Step-by-step explanation:

the step by step explanation is given in the picture.