Systems of Equations - Linear

We discussed the online test that all students should have finished at least once by today. Students are encouraged to retest their *missed problems* to raise their score. I do not suggest that students completely retake a *new* test. They should build on the test that they already answered some of the problems correctly. I will record and only use the highest score that they achieve. At this time, I have not received a test score from every student. They have until midnight to complete a test and not receive a ZERO for this week's assignment.

Today's lesson is review of 8th grade concepts: solving systems of linear equations. Their handout has directions and examples for solving a system of linear equations with three different methods.

Solving a System by Graphing:

• Step 1: Graph each equation on the same coordinate plane.


• Step 2: Identify where the two graphs meet (if anywhere). The point where the graphs meet is a solution of the system. It is possible for the two lines to be parallel and never intersect. Parallel lines have no common points, so the system has no solution.


• Step 3: Check the solution by substituting the values of x and y into both equations. Verify that it solves both equations.


• Example:

Solving a System by Substituting:

• Step 1: Solve one of the equations for either of its variables.


• Step 2: Substitute the expression from step 1 into the other equation and solve for the other variable.


• Step 3: Substitute the solved value from step 2 into either of the original equations and solve for the remaining variable.


• Step 4: Check the solution by substituting the values of x and y into both equations. Verify that it solves both equations.


• Example:

Solving a System by Eliminating:

• Step 1: The goal is to make one of the variables have opposite values for its coefficients in the two equations (like -5x and +5x ... or +4y and -4y). If the equations do not already have this requirement, then select one of the variables to affect. Multiply everything in the equation to get the desired coefficient on the selected variable. You may need to multiply both equations by different values to meet this requirement.


• Step 2: Add the two equations together by collecting like terms. Some students remember this step from last year when they wanted to either get "0x" (zero-x, but called ox) or "+ 0y" (plus zero-y, but called toy). Solve for the remaining variable.


• Step 3: Substitute the solved value from step 2 into either of the original equations and solve for the remainging variable.


• Step 4: Check the solution by substituting the values for x and y into both equations. Verify that it solves both equations.
• Example: Note ... the step numbers in the example below are each one value higher than the way I numbered my steps above.
  
  
  

Homework: Worksheet on Systems of Linear Equations

---