Expressions and Equations / Solving Systems of Equations Algebraically

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.

Answer: 10 adult tickets and 4 child tickets.

The Big Idea

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 \(b\).

What are the students doing?

Students explore a variety of contexts for a linear combination of two quantities with a given constraint.

What is the teacher doing?

Encourage students to explore the exchange between the two quantities and how that exchange maps out the solution on a coordinate grid.