# Ch 8: Common Core HS Algebra: Systems of Equations

Find lessons for high school algebra. These lessons meet the Common Core Mathematics standards for systems of equations (CCSS.Math.Content.HSA-CED.A.3; CCSS.Math.Content.HSA-REI.C.5; CCSS.Math.Content.HSA-REI.C.6; CCSS.Math.Content.HSA-REI.C.7; CCSS.Math.Content.HSA-REI.D.11)

Standard: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. (CCSS.Math.Content.HSA-CED.A.3)

Standard: 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. (CCSS.Math.Content.HSA-REI.C.5)

Standard: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. (CCSS.Math.Content.HSA-REI.C.6)

Standard: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. (CCSS.Math.Content.HSA-REI.C.7)

Standard: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. (CCSS.Math.Content.HSA-REI.D.11)

Students who have mastered these standards are able to explain and demonstrate what a system of equations is and how it is properly used. When applying mastery of these standards, students are able to solve linear and non-linear equations through graphing.

Lessons in this standard cover concepts such as:

• Using substitution and linear combinations to solve systems of linear equations
• Explaining how constraint is used when working with systems of equations
• Finding solutions in a system with constraints
• Identifying solutions for systems of equations with a quadratic and a linear equation

Students demonstrate mastery of these standards when they're attempting to compare two or more equations. This mastery is also showed when they're able to come up with a solution for a system of equations by identifying the intersection point on a graph.

### How to Use These Lessons in Your Classroom

Here are some tips for how to use the lessons to support instruction in these standards:

#### Using System of Equations Lessons

Exhibit the video lesson 'How Do I Use a System of Equations?' Have your students take our quiz that supplements our video lesson for homework. When they return to class the next day, spend time going over each quiz question. Use this time to make sure that each student understands the concepts by having them participate in explaining how each question is solved.

#### Solving Systems of Equations by Graphing Lessons

Create a worksheet containing several systems of equations. Include a sheet of graphing paper when you pass out the worksheet. Present the videos related to graphing systems of equations to students. As a class, go over a few problems before assigning the rest of the worksheet for homework.

#### Solving Systems of Linear Equations Lessons

Spend a few days showing and explaining the different video lessons that cover how to solve several types of systems of linear equations. After completing the systems of linear equations video lessons, help your students develop an understanding of this topic by working through the practice problems and quiz we provide in our 'Practice Solving Systems of Linear Equations' video lesson.

2 Lessons in Chapter 8: Common Core HS Algebra: Systems of Equations
Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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