X- Mathematics : Chapter: Linear Equations in two Variables IMPORTANT CONCEPTS 1. EQUATION: The statement of equality is called an equation. 2. Linear equation in one variable: An equation of the form ax+b=0,where a,b are real numbers,(a≠0) is called a linear equation in one variable. 3. Linear equation in two variables: An equation of the form ax+by+c=0, where a,b,c are real numbers(a≠0,b≠0)is called a linear equation in two variables x and y. 4. Consistent system of linear equations: A system of two linear equations in two unknowns is said to be consistent if it has at least one solution. 5.Inconsistent system of linear equations: if a system has no solution, then it is called inconsistent. The system of a pair of linear equations a1 x+b1 y+c1 =0 a2 x +b2y+c2 =0 (i) has no solution. If a1/a2 = b1/b2 ≠ c1/c2 (ii) has an infinite number of solutions If a1/a2 = b1/b2 = c1/c2 (iii) has exactly one solution. If a1/a2 ≠ b1/b2 6. Algebraic methods: (i)Method of substitution (ii)Method of elimination by addition or subtraction (iii) Method of cross multiplication for: a1 x+b1 y+c1 =0 a2 x +b2y+c2 =0 X= (b1c2 – b2c1) /(a1b2 – a2b1) , y = (c1a2 – c2a1) / a1b2 - a2b1