SOLUTION: Could you please help me solve and place it into the ordered pairs? y=3^5x+1 y=9^-x

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Question 151210: Could you please help me solve and place it into the ordered pairs?
y=3^5x+1
y=9^-x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system

system%28y=3%5E%285x%2B1%29%2Cy=9%5E%28-x%29%29


Since "y" is equal to both 3%5E%285x%2B1%29 and 9%5E%28-x%29, this means that 3%5E%285x%2B1%29=9%5E%28-x%29. Here's another way you can think about it:


y=9%5E%28-x%29 Start with the second equation.


3%5E%285x%2B1%29=9%5E%28-x%29 Plug in y=3%5E%285x%2B1%29. In other words, replace "y" with 3%5E%285x%2B1%29


3%5E%285x%2B1%29=%283%5E2%29%5E%28-x%29 Rewrite 9 as 3%5E2


3%5E%285x%2B1%29=3%5E%282%28-x%29%29 Multiply the exponents.


3%5E%285x%2B1%29=3%5E%28-2x%29 Multiply.


Since the bases are equal, the exponents are equal. So this means that

5x%2B1=-2x


5x=-2x-1 Subtract 1 from both sides.


5x%2B2x=-1 Add 2x to both sides.


7x=-1 Combine like terms on the left side.


x=-1%2F7 Divide both sides by 7 to isolate x. This is the first part of the answer.


y=9%5E%28-x%29 Go back to the second equation (either equation will do)


Plug in x=-1%2F7


Multiply. This is the second part of the answer.


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Answer:

So the answer is x=-1%2F7 and


which approximate to x+=+-0.14286 and y+=+1.36874

So the answer forms the ordered pair which is approximately