Linear Equations in Two Variables
Concepts Learning Sessions
Before delving into the concepts of Linear Equations in two variables, its important to revisit the basics of Algebra - terms, expressions and
definition and types of Polynomials. In this session following topics have been covered:
- Terms and Expressions
- Polynomials and their types
- Linear Polynomials
- Linear Equations in two variables
- Why is a Linear Equation called so?
- Meaning of solution of a Linear Equation
- A pair of Linear Equations
- Methods of Solving a pair of Linear Equations.
- Graphical Method
- Algebraic Method : (Methods of Substitution and Elimination have been discussed in this session)
Session # 2 What are Determinants?
In this session, a small introduction to Determinants has been made. Cramer's Rule to solve a system of linear equations require the knowledge of Determinants and the method of finding its value. This session would not be sufficient for in-depth knowledge in Determinants.
Session # 3 Cramer's Rule
In this session, a method of solving a pair of linear equations in two variables using Cramer's Rule has been described.
Demonstration Sessions
Session # 1 How does the graphical representation of a linear equation in two variables ax+by+c=0 change when the coefficients a, b and c are changed. The rotation and the translation of the graphs has been demonstrated. You can also check what happens to the graph when 'c' becomes zero.
Problems
Problem Solving Session# 1 Solving a pair of linear equations in two variables using the method of "SUBSTITUTION"
Problem Solving Session# 2 Solving a pair of linear equations in two variables using the method of "ELIMINATION"
Problem Solving Session# 3 Solving a pair of linear equations in two variables using the method of "CROSS MULTIPLICATION"
Problem Solving Session# 4 Word Problem on Area of a Rectangle
Problem Solving Session# 5 Consistency of a System of Linear Equations in Two Variables
Problem Solving Session# 6 Consistency of a System of Linear Equations in Two Variables
Problem Solving Session# 7 Solving a system of non-linear equations reducible to linear form
Problem Solving Session# 8 Word Problem on fractions. "The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are reduced by 1, the numerator becomes half the denominator. Determine the fraction."
Problem Solving Session# 9 Word Problem on numbers and digits. "A two digit number is 3 more than 4 times the sum of digits. If 18 is added to the number, the digits are reversed. Find the number."
