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- HSA-REI.C.5Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
- HSA-REI.C.6Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
- HSA-REI.C.7Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = -3x and the circle x<sup>2</sup> + y<sup>2</sup> = 3.
- HSA-REI.C.8(+) Represent a system of linear equations as a single matrix equation in a vector variable.
- HSA-REI.C.9(+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

Stacking Cups: Systems of Equations Real World Application

Algebra I

» Unit:

Systems of Linear Equations

Big Idea:Students use data to create equations describing a concrete scenario. Students analyze the equations as a system to solve a problem.

Solving Linear Equations in Two Variables

Algebra I

» Unit:

Making Informed Decisions with Systems of Equations

Big Idea:This MAP Classroom Challenge provides students with an engaging and thought-provoking activity about notebooks, pens and cash registers to learn about solving equations in two variables!

Graphing Systems of Equations

Algebra I

» Unit:

Making Informed Decisions with Systems of Equations

Big Idea:Students use technology to create and interpret systems of equations graphically!

Solving Systems by Graphing

Algebra I

» Unit:

Systems of Equations

Big Idea:As students gain confidence in graphing - and interpreting the intersection points on - systems of equations, we continue to see how this skill relates to guess and check.

How Far Can Substitution Take You?

Algebra I

» Unit:

Systems of Equations

Big Idea:We'll practice the use of substitution while learning that attention to detail is paramount. Then students will see a problem that's just not so easy to solve by substitution...

Three Ways to Solve a Problem

Algebra I

» Unit:

Systems of Equations

Big Idea:Over the course of today’s lesson, students will beg for an algebraic solution, understand on their own why it’s great that algebra was invented, and see the beauty of an elegant solution.

Mastery Session: MP1, 5.1, and 5.2

Algebra I

» Unit:

Systems of Equations

Big Idea:When students are given time to work at their own pace, without the pressure of a "quiz," they can make the most of an opportunity to show what they can do.

Sweet Problems with Two Variables

Algebra I

» Unit:

Systems of Equations

Big Idea:When we're working on "classic elimination problems" it's important to recognize whether we're looking for an unknown cost or an unknown quantity.

An Intersection Point, and What Happens Around It

Algebra I

» Unit:

Systems of Equations

Big Idea:Often the truest solution to a problem is that "it depends". Substitution is an efficient method for finding the precise intersection of two lines; a graph makes it clear what happens on either side of that point.

Alternate Method to Solve a System of Equations by Substitution

Algebra I

» Unit:

Systems of Equations

Big Idea:Students review the steps of solving a system of equations by substitution by alternating steps as they solve problems in pairs or groups.

The Best of 2 Cell Phone Plans

Algebra I

» Unit:

Systems of Equations

Big Idea:The purpose of this lesson is for students to understand how to analyze a system of equations to determine when a plan is cheaper, more expensive, or cost the same at certain points on the graph.

Creating and Interpreting Equations to Solve Systems

Algebra I

» Unit:

Making Informed Decisions with Systems of Equations

Big Idea:Students create systems of equations and attempt to solve them as an introduction to the relevance of solving systems of equations and inequalities!

REALLY BIG IDEAS! Graphing vs. Substitution

Algebra I

» Unit:

Systems of Equations

Big Idea:If you’re going to have a variety a tools, it’s a good idea to have a good idea of what each is good for!

Quarters, Dimes and Linear Combinations

Algebra I

» Unit:

Systems of Equations

Big Idea:Students start with a concrete problem as they define constraints and progress to the abstract level of solving using algebraic methods. .

From Graphing to Substitution

Algebra I

» Unit:

Systems of Equations

Big Idea:It’s amazing to get to the point where students truly understand how useful and beautiful algebra can be. Transitioning from graphing systems to solving by substitution is an opportunity to get kids there.

HSA-REI.C.5

Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

HSA-REI.C.6

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

HSA-REI.C.7

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = -3x and the circle x^{2} + y^{2} = 3.

HSA-REI.C.8

(+) Represent a system of linear equations as a single matrix equation in a vector variable.

HSA-REI.C.9

(+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).