# Expressions and Equations / Solving Systems of Equations Algebraically

Activity 17 of 18
In this lesson students will investigate pathways for solving systems of linear equations algebraically.

## Planning and Resources

Objectives
Students should be able to use algebraic techniques to solve a system of linear equations in two variables, in particular the methods of elimination and substitution and determine elegant approaches to finding a solution.

Vocabulary
system of linear equations in two variables
substitution
solution to a system

Standard:

## Lesson Snapshot

#### Understanding

Students understand that the initial strategic goal in solving systems of linear equations is to produce a single linear equation in one variable that can be solved and used for substitution back into the system.

### What to look for

Students are gaining flexibility in solving systems of equations and recognizing patterns that indicate which method is most efficient for a given system.

### Sample Assessment

Mary is buying tickets for a movie.

• Each adult ticket costs $9. • Each child ticket costs$5.
• Mary spends \$110 on tickets.
• Mary buys 14 total tickets.
What are the total number of adult tickets and total number of child tickets that she buys?

Develop linear combinations of two quantities and investigate what happens when a constraint is imposed on the linear combination $$ax+by$$ for a given $$a$$ and $$b$$.