Answer:
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!
