Are there any real number solutions to the system y=4 and x²+y²=2? support your findings both analytically and graphically.

The system has no real solution.

Step-by-step explanation:

Hi there!

We have the following equations system:

x² + y² = 2

y = 4

Let´s replace y = 4 in the first equation and solve it for x:

x ² + 4² = 2

x² + 16 = 2

Substract 16 from both sides of the equation

x² = 2 - 16

x² = -14

There is no real number that satisfies this equation, then, the system has no real solution. That means that both curves don´t intersect.

The expression x² + y² = 2 is a circumference of radius √2 with the center in the origin and y = 4 is a straight horizontal line at y = 4(see attached graphic).

Have a nice day!

the circumference is c≈245.04