​Graphs:

​A graph of an equation has no real solution if there is no point of intersection on the graph between the curve itself and the x-axis.

​The equation y=x^2+1 does not intersect the x -axis. Therefore, no value of x will satisfy the equation x^2+1=0 . Thus, this equation has no real solution.

​Using Algebra:

Does the equation y=x^2+1 have a real solution? (Start by setting y=0)

​Systems:

Is there an x value that can make both equations true at the same time?

​How many real solutions?

You can solve graphically or algebraically.