The purpose of this activity is for students to practice combining like terms for expressions that are similar to what students will see when solving systems of equations by elimination. Students will need to add or subtract expressions to eliminate a variable. This activity gives students the chance to practice that skill. Combining like terms to create equivalent expressions gives students the chance to reason abstractly and quantitatively (MP2).

The goal of this discussion is to see how combining like terms in expressions can be useful in solving equations.

Direct students’ attention to the reference created using Collect and Display. Ask students to share their process for combining like terms. Invite students to borrow language from the display as needed. As they respond, update the reference to include additional phrases.

Select students to share their solutions, including any intermediate steps they used to arrive at their answer. Some questions for discussion:

• "Would you rather use the expression or the equivalent expression to find the value when you know that and ?" (The shorter expression that has combined like terms would be easier to use.)
• "Use the values  to find the value of the original expressions and the value of your answers. What do you notice? Why do you think that is?" (The values of both expressions are the same since the expressions are equivalent.)

In this activity, students solve a system of equations by graphing and then include a third—vertical or horizontal—line through the solution point. In the associated Algebra 1 lesson, students will graph equations in a system and additional equations that arise from the elimination method to show that they all intersect at the solution. As students represent the solution to each system of equations with a vertical or horizontal line, they are expressing regularity in repeated reasoning (MP8).

To focus on the work of the activity, it is recommended that students have access to Desmos or another graphing tool to more quickly and accurately find the solutions to the system of equations through graphing. If students need practice graphing lines representing equations by hand or if digital access is not available, the print version provides a graph with one of the lines given and asks students to graph the second line by hand.

The purpose of the discussion is for students to recognize that, for a system of equations represented by graphs that intersect at , the lines and also go through the solution. Select students to share their solutions, including students who found vertical as well as horizontal lines through the intersection point.

Here are some questions for discussion:

• "How could you use your answers to these questions to write another system of equations that have the same solution as the original system of equations?" (The system  has the same solution as the original system  since all 4 lines go through the point .)
• "Two lines intersect at the point . How could you know whether the equation is represented by a line that goes through that same point?" (Substitute the value 3 for and 5 for . If the equation is still true, then the associated line will go through the same point. If the equation is false, then the associated line will not go through the same point.)