Question

Determine how many solutions the system has.
y = x + 2
y = x^2 + 2x + 1

Answer 1

The system can be presented just as a function of x, so for every x for which the following statement

x+2=(x+1)^2 is true the system as described above should be true

x^2+x-1=0, x(x+1)=1 where x is a Real number has no real solution

Answer 2

Answer: two real solutions.

Explanation:

When you graph the system of equations (which has a linear equation and a quadratic equation), you obtain the graph shown attached, which shows a line and a parabola.

As you can see the line and the parabola intersect each other at two points.

By definition, when they intersect then you can conclude that the system of equations have two real solutions.