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Q.
The number of ordered pairs (x, y) satisfying $3^{x} . 5^{y} = 75$ and $3^{y} . 5^{x} = 45$ is
Linear Inequalities
Solution:
The equation are $3^{ x } \cdot 5^{ y }=75 \ldots(1)$
and $3^{ y } \cdot 5^{ x }=45.....$(2)
Dividing the two equations, we get
$\left(\frac{3}{5}\right)^{ x - y }=\frac{75}{45}=\frac{5}{3}$
$ \Rightarrow x - y =-1 .....$(3)
Multiplying equations (1) and (2), we get
$(15)^{ x + y }=45 \times 75=(15)^3$
$ \Rightarrow x + y =3......$(4)
solving $(3)$ and $(4)$ we get $x=1, y=2$