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