# 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."