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

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.

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).

Example 1: Solve the system of linear equations.

Example 2: Solve the system of linear equations.

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

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

Example 4: Solve the system of linear equations.

U-TRY #1 Solve. 1) 3) 2) 4)

Example 5: Solve the system by graphing.

Example 6: Solve the system of linear equations.

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.

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

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?

Homework Pg 506#s 1-55 EOO