Linear Equations and Inequalities (Elementary Math Algebra)
About this ebook
Chapter 8: Linear Equations and Inequalities
In Chapter 8, we focus on Linear Equations and Inequalities, exploring techniques for solving systems of equations and understanding inequalities. These concepts are fundamental for solving real-world problems in fields such as economics, engineering, and science, and are critical for mastering higher-level algebra.
What You'll Learn:
Simultaneous Linear Equations: Learn how to solve systems of linear equations, where two or more equations are solved together to find the values of the variables that satisfy all equations simultaneously. You'll practice solving these systems using different methods, which are essential for dealing with complex algebraic problems.
The Elimination Method: Master the elimination method, which involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other. This technique is especially useful when dealing with larger systems of equations and helps simplify the process of finding solutions.
The Substitution Method: Discover the substitution method, where you solve one equation for a variable and substitute that expression into another equation. This approach provides a clear and straightforward way to solve systems of equations, particularly when one of the equations is easy to manipulate.
Linear Inequalities: Understand how to solve linear inequalities, which are similar to equations but with inequalities (>, <, ≥, or ≤) instead of equal signs. You'll learn how to solve for the variable and graph the solution on a number line.
Number Line and Inequalities: Learn how to represent solutions to inequalities on a number line. This visual tool helps you understand the range of values that satisfy the inequality, making it easier to interpret and solve problems involving inequalities.
By the end of this chapter, you'll be proficient in solving systems of linear equations using both the elimination and substitution methods. Additionally, you'll be able to solve and graph linear inequalities, a crucial skill for dealing with real-life problems where multiple conditions must be satisfied. With step-by-step examples, practice problems, and clear explanations, you’ll be well-equipped to handle these important algebraic topics.
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About the author
Lee Jun Cai is the founder of AcesMath!, an educational centre that coaches students to excel in the field of Mathematics. He specialises in helping with Mathematics papers under GCE O/A - Level and International Baccalaureate.
Mr Lee graduated with a First-Class Honours as a Bachelor of Science from National University of Singapore (NUS). As a student, he won numerous prestigious awards like Tan Teck Chwee Book Prize (Best student in Pure Mathematics) and the D D Chelliah Gold Medal (Best student in Mathematics).
After graduating, Mr Lee enrolled in National Institute of Education for his Post Graduate Diploma of Education specialising in Junior College and Secondary School Mathematics education. He started his teaching career with his alma mater Raffles institution (Year 5 and 6) and moved on to teaching in Catholic Junior College. While teaching in schools, Mr Lee also furthered his studies graduating with Master of Science in Mathematics from NUS.
Embracing continuous learning and improvement, Mr Lee also furthered his studies with an International Baccalaureate Category Two certification.
