Solving Linear Systems of Equations with Elimination (Day 2 of 3)

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Objective

SWBAT solve systems of equations using elimination.

Big Idea

Students will investigate properties of equality with scaled numbers. Students will use multiplication to create zero pair coefficients.

Do-Now

10 minutes

Today I hope that my students will complete the Do Now in about five minutes. In order to keep us on schedule, a hint was provided for today's Do-Now with respect to the new procedure, Elimination.

After five minutes I will ask two students to come up to the board to show their answers to the class. I will ask that each student solve the system using a different method. After they finish, I will ask the class to analyze their work to see if the students arrived at the same answer.

Next, I will ask a student will read the objective, "SWBAT solve systems of equations using elimination".

Before moving on, I will ask students to summarize what we learned about elimination during yesterday's class. Before moving forward, I will return the graded Exit Cards to students from our last class. We will review the responses as a whole group.

Investigation

10 minutes

My plan is for students to complete the Elimination Investigation with a partner. This activity was designed to address two misconceptions that students commonly possess when they begin to solve systems of equations with elimination. 

One goal of this activity is for students to discover that the value of a solution doesn't change when the entire equation is multiplied by a scale factor. The second aim is for students to understand that this congruence only exists when ALL terms are multiplied by the same scale factor.

After 5 minutes we will reconvene as a whole class to have a discussion about our responses. I will ask students to brainstorm how scaling an equation could be advantageous to an Algebra student.

Guided Notes + Practice

30 minutes

Students will follow along during today's lesson with Guided Notes. Students will copy the text below on their notes:

  • We can solve systems of equations by eliminating a _variable_.
  • _A variable_ will eliminate when their _coefficients_ form a  zero pair when added_.
  • If a variable doesn’t eliminate on its own, you have to use _multiplication_ to create your own _zero pair_. 

I will ask students to solve Example One with elimination without encouraging them to scale one of the equations. I expect that my students will be quick to see that nothing will eliminate with addition, or even when the signs are changed in one equation.

Next, I will ask students to recall what we discovered in our Elimination Investigation. I will tell students that we can use that the procedure that was completed during the Investigation to alter one equation in a system so that the coefficients form a zero pair. For example, if we examine both sets of variables, 5y and -3y have nothing in common but -3x and 6x do. If we multiply the top equation by two, we will have created a zero pair. After multiplying the top equation by 2, we will finish solving the system.

We will then solve Example Two and the You Try problems. Examples Three and Four contain the same system of equations. I will solve the problem once by eliminating x, and a second time by eliminating y.

Partner Activity - Matching

20 minutes

Students will practice solving systems of equation using elimination in today's Partner Activity. Students will organize the cards into groups of three (original system, scale factor, solution). I will observe my students as they work looking to see if students:

  • examine each system of equations carefully
  • determine if one equation in the system needs to be manipulated with multiplication in order to create a zero pair of coefficients for a variable
  • solve the system correctly. 

 

Teaching Note: This activity needs to be cut out and shuffled by the instructor before class begins.

Closing

10 minutes

I will ask a volunteer to summarize what we did in class today. Then, I will ask the class to reflect upon the importance of knowing how to solve a system using three different methods. I will ask them to justify their reasoning. 

 Students will then complete an Exit Card.