# Ch 19: PLACE Mathematics: Systems of Equations

### About This Chapter

## PLACE Mathematics: Systems of Equations - Chapter Summary

This chapter can help you review material on systems of equations in preparation for the PLACE Mathematics exam. Watch our expert instructors as they demonstrate how to solve problems with linear systems, write augmented matrices for linear systems and solve non-linear systems of equations. After watching the lesson videos in this chapter, you should be prepared for test questions on:

- Solving systems of linear equations in two variables
- Systems of linear equations with three variables that have solutions
- Systems of linear equations with three variables that have infinite or no solutions
- Augmented matrices of for linear systems
- Using determinants to solve systems of linear equations in two and three variables
- Solving systems of equations consisting of quadratic equations

As you watch these lesson videos, you can send any questions you may have on systems of equations to our instructors for clarification if you need it. You can also complete lesson quizzes to help reinforce the material and find out what you might need to re-review before taking the PLACE Mathematics exam. If you need to target a specific topic, use the video tags in the timeline or check out the video transcript.

### PLACE Mathematics: Systems of Equations Objectives

PLACE Mathematics is the certification exam for math teachers in the state of Colorado. As you prepare for the paper-based certification exam, keep in mind that the test consists of a series of multiple-choice questions for which test takers are given 4.5 hours to complete. Of these multiple-choice questions 19% are on the foundations of mathematics and 24% are on the functions and relations. You may find questions related to this chapter in both of these sections.

### 1. How to Solve a System of Linear Equations in Two Variables

Watch this video lesson to learn how you can solve a system of linear equations in two variables by using the substitution method. Learn how easy it is to use on any linear system in two variables.

### 2. How to Solve a Linear System in Three Variables With a Solution

After watching this video lesson, you will be able to solve a linear system in three variables using the elimination method. Learn the simple operations that are needed to solve your system.

### 3. How to Solve a Linear System in Three Variables With No or Infinite Solutions

In this video lesson, you will learn to recognize when a linear system has no solution or an infinite number of solutions. You will also learn how to go about solving each of these types of systems.

### 4. How to Write an Augmented Matrix for a Linear System

Watch this video lesson to learn how you can turn your system of equations into matrix form. The matrix form is another way of writing your linear system that is sometimes easier to work with.

### 5. Solving Systems of Linear Equations in Two Variables Using Determinants

Watch this video lesson to learn how you can easily find the solution of a linear system in two variables by just using determinants. All you need to find the complete solution is to find three determinants.

### 6. Solving Systems of Linear Equations in Three Variables Using Determinants

Watch this video lesson to learn how to use Cramer's rule to help you find your solutions by finding just four determinants. Learn the numbers to use for your determinants.

### 7. Solving Non-Linear Systems of Equations

Many systems of equations are non-linear, and knowing how to solve these non-linear systems is important. In this lesson, learn how to recognize and solve non-linear systems of equations.

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### Other Chapters

Other chapters within the PLACE Mathematics: Practice & Study Guide course

- PLACE Mathematics: Properties of Real Numbers
- PLACE Mathematics: Fractions
- PLACE Mathematics: Decimals & Percents
- PLACE Mathematics: Ratios & Proportions
- PLACE Mathematics: Measurements & Conversions
- PLACE Mathematics: Logic
- PLACE Mathematics: Mathematical Reasoning
- PLACE Mathematics: Vector Operations
- PLACE Mathematics: Matrices & Determinants
- PLACE Mathematics: Exponents & Exponential Expressions
- PLACE Mathematics: Algebraic Expressions
- PLACE Mathematics: Linear Equations
- PLACE Mathematics: Inequalities
- PLACE Mathematics: Absolute Value Problems
- PLACE Mathematics: Quadratic Equations
- PLACE Mathematics: Polynomials
- PLACE Mathematics: Rational Expressions
- PLACE Mathematics: Radical Expressions
- PLACE Mathematics: Complex Numbers
- PLACE Mathematics: Functions
- PLACE Mathematics: Graphing Piecewise Functions
- PLACE Mathematics: Exponential and Logarithmic Functions
- PLACE Mathematics: Continuity of Functions
- PLACE Mathematics: Limits
- PLACE Mathematics: Rate of Change
- PLACE Mathematics: Calculating Derivatives & Derivative Rules
- PLACE Mathematics: Graphing Derivatives & L'Hopital's Rule
- PLACE Mathematics: Applications of Derivatives
- PLACE Mathematics: Area Under the Curve & Integrals
- PLACE Mathematics: Integration & Integration Techniques
- PLACE Mathematics: Integration Applications
- PLACE Mathematics: Foundations of Geometry
- PLACE Mathematics: Introduction to Geometric Figures
- PLACE Mathematics: Properties of Triangles
- PLACE Mathematics: Triangles, Theorems & Proofs
- PLACE Mathematics: Parallel Lines & Polygons
- PLACE Mathematics: Quadrilaterals
- PLACE Mathematics: Circular Arcs & Circles
- PLACE Mathematics: Conic Sections
- PLACE Mathematics: Geometric Solids
- PLACE Mathematics: Analytical Geometry
- PLACE Mathematics: Using Trigonometric Functions
- PLACE Mathematics: Trigonometric Graphs
- PLACE Mathematics: Solving Trigonometric Equations
- PLACE Mathematics: Trigonometric Identities
- PLACE Mathematics: Sequences & Series
- PLACE Mathematics: Graph Theory
- PLACE Mathematics: Set Theory
- PLACE Mathematics: Overview of Statistics
- PLACE Mathematics: Summarizing Data
- PLACE Mathematics: Tables & Plots
- PLACE Mathematics: Probability
- PLACE Mathematics: Discrete Probability Distributions
- PLACE Mathematics: Continuous Probability Distributions
- PLACE Mathematics: Sampling
- PLACE Mathematics: Hypothesis Testing
- PLACE Mathematics: Regression & Correlation
- PLACE Mathematics Flashcards