Given a circle described by the equation:

and a function g(x) given by the table

The function g(x) describes a straight line with the equation:

To check if the circle and the line intersects, we substitute the equation of the line into the equation of the circle to see if we have a real solution.
i.e.

When x = 6, y = 2(6) - 20 = 12 - 20 = -8 and when x = 10, y = 2(10) - 20 = 20 - 20 = 0
Therefore, the circle and the line intersect at the points (6, -8) and (10, 0).
Answer:
sum of twice a number and three is 21
2x + 3 = 21
x = 9
3x-5y =15
2x-y=-4
multiply the equation by 5 and then subtract equation 2 from equation 1
so 3x-5y =15
10x-5y =-20
-7x =35 x =-5
plug in the value of x in the second equation -10 -y =-4 - y= -4 +10 y =-6
x=-5 y=-6