Pair of Linear Equations in Two Variables Class 10 Notes Maths: Chapter 3
Pair Of Linearequations Intwo Variablesa
- A pair of linear equations in two variables x and y, can be algebraically represented as : a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0.Here a1, b1, c1, a2, b2 and c2 are real numbers and a12 + b12 ≠ 0 and a22 + b22 ≠ 0.
- There are two methods of solving a pair of linear equations :
(i) Graphical method, and
(ii) Algebraic method.
- A pair of linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 graphically or geometrically represents a pair of straight lines which are :
(i) intersecting, if a1/a2≠b1/b2
(ii) parallel, if a1/a2≠b1/b2 ≠c1/c2
(iii) coincident, if a1/a2=b1/b2 =c1/c2
- While solving a pair of linear equations by the graphical method, we have to first draw the lines represented by them on the graph.
(i) If the resultant line intersect, then the pair is said to be consistent and the coordinates of the point provide an unique solution.
(ii) If the lines are parallel, then they do not have any solutions and are called inconsistent.
(iii) If the lines are coincident, then there are infinite numbers of solutions and they are called consistent but having infinite solutions.
- A pair of linear equations can be solved by the algebraic method in three ways :
(i) By substitution method,
(ii) By elimination method
- For a pair of linear equations in two variables
a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0
(i) if,a1/a2≠b1/b2then the pair of linear equations represents a consistent and unique solution;
(ii)if, a1/a2=b1/b2≠c1/c2then the pair of linear equations represents an inconsistent solution; and
(iii) if,then the pair of linear equations represents consistent but infinite Solution