Solve this system of equations. Hint: Use graphing, substitution, or elimination to find the points (x,y) that make both equations true.(pic attached)

Question

Solve this system of equations.  Hint: Use graphing, substitution, or elimination to find the points (x,y) that make both equations true.(pic attached)

anonymous · Answer

attachment

campbell_st · Answer

the circle has a centre at the origin and radius of 8

the ellipse has a centre at the origin and major axis  length of 8
minor axis length of 1

the points of intersection are (-8, 0) and (8, 0)

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campbell_st · Answer

algebraically 

since both equations are equal to 64 equate them 


$$x^2 + y^2 = x^2 + 64y^2 = 63y^2 = 0$$

then y = 0

substitute into the circle

x^2 + 0 = 64

$$x = \pm 8$$