Which graph contains the points of intersections satisfying this linear-quadratic system of equations? x^2+y^2=20 x-y+2=0

  There are two points of intersection (2, 4) and (-4, -2)

Step-by-step explanation:

x - y + 2 = 0     →       x = y - 2

Use Substitution Method:

x² + y² = 20

(y - 2)² + y² = 20              replaced x with (y - 2)

y² - 4y + 4 + y² = 20        expanded (y - 2)²

2y² - 4y + 4 = 20             added like terms

2y² - 4y - 16 = 0               subtracted 20 from both sides

y² - 2y - 8 = 0                  divided both sides by 2

(y - 4)(y + 2) = 0               factored

y - 4 = 0    and      y + 2 = 0       applied Zero Product Property

y = 4        and       y = -2

Input the y-values into x = y - 2 to solve for x.

y = 4;   x = 4 - 2                      y = -2;    x = -2 - 2

           x = 2                                         x = -4

      (2, 4)                                         (-4, -2)