Chapter 3 : PAIR OF LINEAR EQUATIONS IN TWO VARIABLES What is Linear Equation? A linear equation is an algebraic equation in which the highest power of the variable(s) is 1, and its graph always forms a straight line. Example : 3x + 4 = 0 , 3x + 4y = 6 Linear Equation in Two variable: A linear equation in two variables is an equation of the form ax+by+c=0, where a,b,c are real numbers and x,y are variables. Its graph is always a straight line in the coordinate plane. Example : a) 2x + 3y = 6 , b) 4x + 5y = 8. Solution of pair of linear equation in two variable: A pair of linear equations in two variables can be represented, and solved, by the: (i) graphical method (ii) algebraic method a) Graphical method 1. General Form A pair of linear equations in two variables can be written as: a 1 x + b 1 y + c 1 = 0 a 2 x + b 2 y + c 2 = 0 Here, x and y are variables, and (a 1 , b 1 , c 1 , a 2 , b 2 , c 2 ) are constants. 2. Steps in the...

Chapter 2 : Polynomial What is polynomial? A polynomial is an expression made up of variables and coefficients, combined using addition, subtraction, and multiplication, with non-negative integer exponents. Example : 3x 4 -2x 2 +7x-5. Key Features of Polynomial : let's discuss some features of polynomial: Take a polynomial : 3x 4 -2x 2 +7x-5. a) Degree: The highest power of the variable(x)(e.g. degree of 3x 4 -2x 2 +7x-5 is 4). b) Terms: Each part separated by + or – (e.g., 3x 4 , -2x 2 , 7x, -5). c) Coefficients: Numbers multiplying the variables (e.g., 3, -2, 7). d) Constant term: The standalone number (e.g. -5). Types of polynomial: a) Linear polynomial: A polynomial of degree 1.     Example : 2x – 3 , u + 5 , 3u+ 5 b) Quadratic polynomial : A polynomial of degree 2     Example : 3x 2 +2x – 3 ,3u 2 - u + 5 c) Cubic polynomial : A polynomial of degree 3     Example : 2...