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

### About This Chapter

**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)

## About This Chapter

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.

### 1. What is a System of Equations?

So what happens if we want to compare more than one equation? Welcome to a 'system' of equations! Learn what one is, how to solve them and when they come up in real life.

### 2. How Do I Use a System of Equations?

There are a few classic algebra word problems, such as the one about two trains traveling at different speeds. In this lesson, you'll learn how to take a word problem and convert it into the system of equations that will allow you to find the answer using either substitution or elimination.

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

### Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

### Other Chapters

Other chapters within the Common Core Math - Algebra: High School Standards course

- Common Core HS Algebra: Algebraic Expressions
- Common Core HS Algebra: Linear Equations
- Common Core HS Algebra: Linear Inequalities
- Common Core HS Algebra: Quadratics
- Common Core HS Algebra: Exponents and Exponential Functions
- Common Core HS Algebra: Polynomials
- Common Core HS Algebra: Rational and Radical Expressions and Equations
- Common Core HS Algebra: Matrices
- Common Core HS Algebra: Sequences and Series
- Understanding Common Core Standards