Question

A system of equations is given below:

(x+1)^2 + (y-4)^2 = 9
y=x+2

Which choice represents a solution to this system of equations?

A. (-2,0)
B. (1,-1)
C. (2,4)
D. (-1,4)

Answer 1

$A.\ (-2,\ 0)\\\\substitute\ to\ y=x+2\\\\0=-2+2\\0=0\ CORRECT\\\\substitute \ to\ (x+1)^2+(y-4)^2=9\\\\(-2+1)^2+(0-4)^2=9\\(-1)^2+(-4)^2=9\\1+16=9\\17=9\ \ FALSE$

$B.\ (1,\ -1)\\\\substitute\ to\ y=x+2\\\\-1=1+2\\-1=3\ \ \ FALSE$

$C.\ (2,\ 4)\\\\substitute\ to\ y=x+2\\\\4=2+2\\4=4\ \ \ CORRECT\\\\substitute\ to\ (x+1)^2+(y-4)^2=9\\\\(2+1)^2+(4-4)^2=9\\3^2+0^2=9\\9+0=9\\9=9\ \ \ CORRECT$

$D.\ (-1,\ 4)\\\\substitute\ to\ y=x+2\\\\4=-1+2\\4=1\ \ \ \ FALSE$

Answer: C. (2, 4)