How many solutions exist for the system below?
in two or more complete sentences, give the solution and explain how you solved the system.
{ y=-2x+3
{y=-2(3^x)

There are no solutions to this system. If

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

At , the derivative of the line is , whereas the derivative of the exponential is .

Since for all , there can't be other solutions because the exponential is already below the line, and it decreases at a faster rate.

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