pair of linear equation notes class 10 cbse
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Basic Concepts with Examples
• Linear Equation in Two Variables An equation which can be put in the form ax + by + c = 0where a, b and c are real numbers {a, b ≠ 0) is called a linear equation in two variables ‘x’ and ‘y’
• General Form of a Pair of Linear Equations in Two VariablesGeneral form of a linear pair of equations in two variables is: a1x + b1y + cx - 0 and a2x + b2y + c2 = 0where a1 b1, c1, a2, b2, c2 are real numbers such that a12 + b12 0 and a22 + b22 0
• Solution of a Pair of Linear Equations in Two VariablesThe solution of a linear equation in two variables ‘x’ and ‘y’ is a pair of values (one for ‘x’ and other for ‘y’)which makes the two sides of the equation equal.There are two methods to solve a pair of linear equations: (i) algebraic method (ii) graphical method.
• Algebraic MethodWe have already studied (i) Substitution method and (ii) Elimination method. Here, we will study cross-multiplication method also. If a1 x + b1 y + c1 = 0 a2 x + b2 y + c2 = 0form a pair of linear equations, then the following three situations can arise: (i) If then the system is consistent. (ii) If then the system is inconsistent. (ii) If then the system is dependent and consistent.
• Graphical Method of Solution of a Pair of Linear Equations (i) If the graphs of two equations of a system intersect at a point, the system is said to have a unique solution, i.e., the system is consistent. (ii) If the graphs of two equations of a system are two parallel lines, the system is said to have no solution, i.e., the system is inconsistent. (iii) When the graphs of two equations of a system are two coincident lines, the system is said to have infinitely many solutions, i.e., the system is consistent and dependent.
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