Topics
Number Systems
Algebra
Geometry
Trigonometry
Statistics and Probability
Coordinate Geometry
Mensuration
Internal Assessment
Real Numbers
Pair of Linear Equations in Two Variables
 Linear Equation in Two Variables
 Graphical Method of Solution of a Pair of Linear Equations
 Substitution Method
 Elimination Method
 Cross  Multiplication Method
 Equations Reducible to a Pair of Linear Equations in Two Variables
 Consistency of Pair of Linear Equations
 Inconsistency of Pair of Linear Equations
 Algebraic Conditions for Number of Solutions
 Simple Situational Problems
 Pair of Linear Equations in Two Variables
 Relation Between Coefficient
Arithmetic Progressions
Quadratic Equations
 Quadratic Equations
 Solutions of Quadratic Equations by Factorization
 Solutions of Quadratic Equations by Completing the Square
 Nature of Roots of a Quadratic Equation
 Relationship Between Discriminant and Nature of Roots
 Situational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated
 Application of Quadratic Equation
Polynomials
Circles
 Concept of Circle  Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
 Tangent to a Circle
 Number of Tangents from a Point on a Circle
 Concept of Circle  Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
Triangles
 Similar Figures
 Similarity of Triangles
 Basic Proportionality Theorem (Thales Theorem)
 Criteria for Similarity of Triangles
 Areas of Similar Triangles
 Rightangled Triangles and Pythagoras Property
 Similarity of Triangles
 Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
 Triangles Examples and Solutions
 Angle Bisector
 Similarity of Triangles
 Ratio of Sides of Triangle
Constructions
Heights and Distances
Trigonometric Identities
Introduction to Trigonometry
Probability
Statistics
Lines (In Twodimensions)
Areas Related to Circles
Surface Areas and Volumes
 Concept of Surface Area, Volume, and Capacity
 Surface Area of a Combination of Solids
 Volume of a Combination of Solids
 Conversion of Solid from One Shape to Another
 Frustum of a Cone
 Concept of Surface Area, Volume, and Capacity
 Surface Area and Volume of Different Combination of Solid Figures
 Surface Area and Volume of Three Dimensional Figures
notes
In this method there are three conditions
(1)Condition `a_1/a_2` is not equal to `b_1/b_2`
Example `2x+9y+12=0` and `6x+1y+8=0`
`2/6` is not equal to `9/1`
If we represent this equations on graph then the lines of this equation will intersect each other at some point.
In this condition we can conclude
1) We get Intersecting line.
2) Such type of pair of linear eaquation with two variable where `a_1/a_2` is not equal to `b_1/b_2` have only one solution i.e unique solution.
3) This type of equations are called Consistent equations.
(2)Condition `a_1/a_2`= `b_1/b_2`= `c_1/c_2`
Example `2x+4y+8=0` and `6x+12y+24=0`
`2/6=1/3, 4/12=1/3, 8/24=1/3` i.e `1/3=1/3=1/3`
In the graphical representation of this equations the lines wil Coincide.
Thus the conclusion in this condition is
1) We get conincent lines.
2) Such type of pair of linear eaquation with two variable where `a_1/a_2=b_1/b_2=c_1/c_2` have infinitely many soultions.
3) This equation is also called as Consisitent equations.
(3) Condition `a_1/a_2= b_1/b_2` is not equal to `c_1/c_2`
Example `2x+3y+4=0` and `4x+6y+7=0`
`2/4=1/2, 3/6=1/2, 4/7` i.e `1/2=1/2` is not equal to `4/7`
The graphical representation of these equations will result in parellel lines.
Here the conclusion is
1) We will get Parellel.
2) Such type of pair of linear eaquation with two variable where `a_1/a_2= b_1/b_2` is not equal to `c_1/c_2` have no solution.
3) This type of Linear equations which dont give any solution are called as Inconsistent equations.
Video Tutorials
Shaalaa.com  Pair of Linear Equation in two variable part 2 (Graphical Method)
Related QuestionsVIEW ALL [38]
Complete the following table to draw the graph of 2x – 6y = 3:
x  −5  `square` 
y  `square`  0 
(x, y)  `square`  `square` 
Complete the following table to draw the graph of 2x – 6y = 3
x  5  x 
y  x  0 
(x,y)  (5,x)  (x,0) 
Complete the following table to draw graph of the equations  (I) x + y = 3 (II) x – y = 4
x + y = 3
x 
3 

y  5  3  
(x,y)  (3,0)  (0,3) 
x – y = 4
x 

1  0 
y  0  4  
(x,y)  (0,4) 