`x^2 + y = 4, e^x - y = 0` Solve the system graphically or algebraically. Explain your choice of method.

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.