1. Systems of Linear Equations in Two Variables (by Elimination)
Section 7.2
Systems of Linear Equations in Two Variables
(by Elimination)

2. Objective By following instructions students will be able to:
Use the method of elimination to solve systems of equations in two variables.
Graphically interpret the number of solutions of systems of linear equations in two variables.
Use systems of linear equations in two variables to model and solve real-life problems.

3. Systems of Equations
When solving a systems of linear equation, there are three methods to choose from to find the point of intersection.
Graphing (slope intercept form).
Substitution (isolate a variable).
Elimination (additive inverse).

4. Example 1:
Solve the system of linear equations.

5. Example 2:
Solve the system of linear equations.

6. Number of Solutions One Solution The lines intersect
The lines have different slopes.
Consistent, independent
No Solution
Parallel lines
SAME SLOPE, DIFFERENT y-intercepts
inconsistent
Infinitely Many Solutions
SAME LINE
SAME SLOPE and Y-INTERCEPTS
Consistent, dependent

7. Example 3:
Graph each system separately and determine the number of solutions. Then state whether the system is consistent or inconsistent. a) b) c)

8. Example 4:
Solve the system of linear equations.

9. U-TRY #1
Solve.
1) )
2) )

10. Example 5:
Solve the system by graphing.

11. Example 6:
Solve the system of linear equations.

12. Example 7:
An airplane flying into a headwind travels the 2000 mile flying distance between two cities in 4 hours and 24 minutes. On the return flight, the same distance is traveled in 4 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.

13. U-TRY #2
Solve using any method. 1) 2)

14. Revisit Objective Did we…
Use the method of elimination to solve systems of equations in two variables?
Graphically interpret the number of solutions of systems of linear equations in two variables?
Use systems of linear equations in two variables to model and solve real-life problems?

15. Homework
Pg 506#s 1-55 EOO