# Lesson 14

Making More New, True Equations

These materials, when encountered before Algebra 1, Unit 2, Lesson 14 support success in that lesson.

### Lesson Narrative

The purpose of this lesson is to practice combining like terms and finding vertical and horizontal lines that pass through the point representing the solution of a system of equations. In the associated Algebra lesson, students begin the process of understanding solving systems of equations by elimination. When adding or subtracting equations, students need to combine like terms. The first activity after the warm-up gives students a chance to practice that skill. To understand solving by elimination, students in the associated Algebra lesson look at graphs representing various equations that result from adding two equations where one variable is eliminated. In particular, the resulting equations are of the form \(y = a\) or \(x = a\) for a number \(a\). Recalling the appearance of graphs that represent such equations is supported by the second activity in this lesson. Students look for and make use of a structure (MP7) as they use their familiarity with graphs of linear equations to match a graph with an equation, and to solve a system of equations by graphing.

### Learning Goals

Teacher Facing

- Practice combining like terms for expressions that resemble the types seen when solving systems of equations by elimination.
- Write the equation of a vertical or horizontal line that goes through the point that represents the solution to a system of equations.

### Student Facing

- Let’s practice combining like terms and working with horizontal and vertical lines.

### Required Materials

### Required Preparation

Acquire devices that can run Desmos (recommended) or other graphing technology. It is ideal if each student has their own device. (Desmos is available under Math Tools.)