Answer:
A general line can be represented as , y= m x + c
And general equation of circle is , ax²+by²+2 g x +2 f y +c=0
Now there are following possibilities
1. A line and circle have no common point of intersection, that is no solution.
2. A line may be a tangent to a circle, that is one common point, one solution.
3. A line may intersect a circle maximum at two points, that is 2 solution.
Image is depicted below.
For this case we can propose a system of equations:
x: Let the variable that represents the number of small cookies
y: Let the variable that represents the number of large cookies
According to the statement we have:
We multiply the first equation by -2:
We have the following equivalent system:
We add the equations:
We look for the value of the variable "x":
Answer:
They sold 80 small cookies and 50 large cookies