1. Solving Systems Graphically
Section 7-7-A
Solving Systems
Graphically

2. Def: The “solution” will be all points that satisfy
(are on the graph of) both equations.
Ellipse
and
Line
Points of intersection are the solution

3. Possible types of solutions:
No solutions
a.)
2 solutions
b.)
4 solutions
c.)
d.)
4 solutions
e.)
2 solutions

4. Yes, systems of equations are collections of equations
3 solutions
No solutions
g.)
Other possibilities?
Yes, systems of equations are collections of equations
and the possibilities are endless

5. 1) Solve: x2 + 4y2 = 25
2y + x = 1

6. 1) (find solutions using your calculator)
Remember the ellipse is entered as 2 curves
Use the “trace” feature or
2nd Function Calculate- “Intersect”

7. 2.) Find a system of 2nd degree equations with
exactly 3 solutions?
Ellipse
and
Hyperbola
Circle
and
Hyperbola
Ellipse
and

8. Use graphing calculator
3.) Solve: y2 + (x - 5)2 = 9
4x2 - y2 = 36
Use graphing calculator

9. 3.)
Circle and Hyperbola
2 Solutions
(3.225, 2.419)
(3.225, )

10. Homework
Page 459 # 1-8 and page 464 # 5