what is the total number of points of intersection of the graphs of the equations x^2+y^2=16 and y=x?

Question

Please show how to solve it

Answer 1

x² + y² = 4² is the equation of a circle centered at the origin (0,0) with radius 4.

 

There are two intersections with the line y = x

 

2x² = 16 ----> x² = 8 ----> x₁ = √8 =2√2 and x₂ = -2√2

 

The 2 intersections are (2√2, 2√2) and (-2√2, -2√2)