Lesson objective: Write and solve systems of equations from a description, especially those that lead to equations in standard form.

Students bring prior knowledge of writing one or more variable equations from 7.EE.B.4 and 8.F.B.4. This prior knowledge is extended to systems of equations as students write and solve systems from a description. A conceptual challenge students may encounter is solving when the system is not set up to efficiently use substitution.

The concept is developed through work with numerical equations, which help students see and understand where the variables should be placed in the structure of the equations.

This work helps students deepen their understanding of operations because the same operations used with numbers in an equation should be used with variables that take the place of those numbers.

Students engage in Mathematical Practice 8: Students look for and express regularity in repeated reasoning as they notice the structure of numerical equations, and then write two-variable equations to model the changing quantities.

**Key vocabulary:**

- standard form
- system of equations
- transitive property