Solve the following system of equations and show all work. y = −x2 + 4 y = 2x + 1

Y = -x² + 4
y = 2x + 1

Since the right side of both sides are equal to y, we can set them equal.

-x² + 4 = 2x + 1

Now that we just have one variable, we can solve easily.
Let's get everything on one side.

x² + 2x - 3 = 0

Let's solve this quadratic by factoring.
We want two numbers that multiply to -3 and add to 2.
These are 3 and -1. Let's split the middle.

x² - x + 3x - 3 = 0

Factor the first and last two terms...

x(x-1) + 3(x-1) = 0
(x+3)(x-1) = 0

And value of x which causes either factor to equal 0 is a solution.
We can derive these equations:

x+3=0 and x-1=0
Then solving for x...
x = -3 or 1

(1/x + 1)^2 + 6 (1/x + 1) +5