SOLUTION: 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

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Question 1063679: 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
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.


Plots y1 = -2x+3 (red) and y2 = -2*3^x (green)

It looks like there are no solutions.

To prove it, consider the difference y3 = y1 - y2 = %28-2x%2B3%29+-+%28-2%2A3%5Ex%29 = 2%2A3%5Ex-2x+%2B3 and then find its minimum using differentiation.
Then estimate this minimum and show that it is positive.

I didn't try it, but you can.