Precalculus, Chapter 7, 7.1, Section 7.1, Problem 54

You need to solve the system, hence, selecting to solve it algebraically, yields:
x^2 + y = 4
e^x - y = 0
Replacing e^x for y in the first equation yields:
x^2 + e^x = 4
e^x = 4 - x^2
Now, you need to solve for x the equation, using graphical method, hence, you need to trace the curves for the equations y = e^x and y = 4 - x^2, and then you need to find out where these curves intercept each other. Notice that the red curve representing y= e^x and the black curve representing y = 4 - x^2, intercept each other at a point located between [1,2], much closer to the value x = 1.

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