Solving Systems of Equations
Grade Level: Algebra II
Type of Lesson: Problem Solving
Standard
TMP 7.3.c: Solve systems of linear and non-linear equations in two variables.
TMP 7.4.d: Solve 2x2 and 3x3 systems of linear equations
Objectives
Objective 1: Students will solve systems of equations using the properties of equality.
Materials
Paper, pencil, whiteboard or overhead
Anticipatory Set (10 min)
Have students solve the following, describing their solutions geometrically or explaining why there is no solution, as the case may be. This is review from Algebra I, but students may need prompting here. (See Algebra I Standard A1.4.D) x+y = 4 x + 2y = -4 10x – 5y = 25 x – y =1 -2x – 4y = 0 -2x + y = -5
Unique solution. No solution Infinite # of solutions.
Micro lesson: Solving a system of 3 linear equations in 3 variables (20 minutes) x + y –z = 0 x + y +z = 0
-x -y - z = 1
Method
1. Pick a variable to annihilate by using the algebraic rules of equality
2. Annihilate the variable in two pairs of equations.
3. Solve the resulting two equations in two variables.
4. Back solve for the value of the annihilated variable.
Guided Practice
2x + y –z = 0 x + 3y +z = 0 x + y –z = 0 x + y +z = 0 x + y –z = 0 x + y -z = 0
-x -y - z = 1
Unique Solution
-x -y +z = 1 no solution
-x -y - z = 1
Infinite # of solutions
Homework (Problem Solving Exercise; Students may begin in class.)
1. Jimmy Ray and his brother, Bubba, need to raise $75 to get their favorite pig, Big Pink Pam, out of hock. Not having high school diplomas, Jimmy Ray only makes 6 bucks an hour plucking

chickens. His big brother, Bubba, shovels chicken guts into a ditch for 5 bucks an hour. Jimmy
Ray and Bubba agree to work a exactly a combined total of 12 hours to save Big Pink Pam.
How long must each brother work to bring home their pet pig (and future source of head cheese)? (Your method of solution must use systems of equations.)
2. Jimmy Ray and Bubba fight about the total cost of freeing Big Pink Pam. Jimmy still thinks it will take $75, but Bubba insists the pawn broker said $70. Set up two equations that describe the hours worked at the respective rates, one equation for each total amount, and try to solve this two equation system. Why can’t this system be solved?
3. Suppose Jimmy Ray and Bubba each earned twice the hourly rate of pay they currently earn, and freeing Big Pink Pam from the pawn broker’s evil clutches cost $150. However, they still agree to work a total of 12 hours to raise the bail money for their beloved oinker. Is the system of equations any different here? Why or why not?
4. Continue the saga of Bubba, Jimmy Ray, and Big Pink Pam by creating a word problem involving 3 equations and 3 variables. Be ready to present this problem to others in class. Make sure it makes sense, even if it is a bit far fetched! (Hence, your word problem must be very well conceived and well written!)