Question

How many solutions exist for the system below?

Answer 1

Answer:

​The system of equations has no solution. Geometrically speaking, both the lines will never intersect or meet. Hence, no solution exists.

Step-by-step explanation:

Answer 2

There are no solutions to this system. If

$-2x+3 > 0 \iff x < \dfrac{3}{2}$

the line is positive and the exponential is negative, so they can't have any point in common.

At $x = \frac{3}{2}$, the derivative of the line is $-2$, whereas the derivative of the exponential is $-3^x\log(9)$.

Since $-3^x\log(9)$ for all $x>\frac{3}{2}$, there can't be other solutions because the exponential is already below the line, and it decreases at a faster rate.