Math 3 – 208: Systems of Circles
Name: _____________________________
Lesson adapted from Carnegie Learning Math 3 Student Textbook
1
Essential Question:
How can we solve a system of equations that involves a circle?
BUILDING BLOCKS
Earlier this year we discussed solving systems of linear equations, such as the system
+

=

=
5
8
2
x
y
x
y
.
What are some different methods that can be used to solve this system of equations?
How many different solutions will this system have? How do you know your answer is true?
Solve the system
.
INVESTIGATION
Let’s think about a system of equations involving
a line and a circle
How many different solutions could this system have? Sketch a graph of a system that has that number
of solutions. If there are multiple possibilities, make multiple sketches.
Solving Graphically
For each system, sketch the circle and the line on the grid below. Estimate the solution to the
system of equations. Check each solution using the original equations.
.
1.

=
=
+
5
2
25
2
2
x
y
y
x
Math 3 – 208: Systems of Circles
Name: _____________________________