#### Topics

##### Number Systems

##### Real Numbers

##### Algebra

##### Polynomials

##### 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 Co-efficient

##### 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

##### Arithmetic Progressions

##### Coordinate Geometry

##### Lines (In Two-dimensions)

##### Constructions

- Division of a Line Segment
- Construction of Tangents to a Circle
- Constructions Examples and Solutions

##### Geometry

##### Triangles

- Similar Figures
- Similarity of Triangles
- Basic Proportionality Theorem (Thales Theorem)
- Criteria for Similarity of Triangles
- Areas of Similar Triangles
- Right-angled 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

##### 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

##### Trigonometry

##### Introduction to Trigonometry

- Trigonometry
- Trigonometry
- Trigonometric Ratios
- Trigonometric Ratios and Its Reciprocal
- Trigonometric Ratios of Some Special Angles
- Trigonometric Ratios of Complementary Angles
- Trigonometric Identities
- Proof of Existence
- Relationships Between the Ratios

##### Trigonometric Identities

##### Some Applications of Trigonometry

##### Mensuration

##### Areas Related to Circles

- Perimeter and Area of a Circle - A Review
- Areas of Sector and Segment of a Circle
- Areas of Combinations of Plane Figures
- Circumference of a Circle
- Area of Circle

##### Surface Areas and Volumes

- 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

##### Statistics and Probability

##### Statistics

##### Probability

##### Internal Assessment

## 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 these equations on a graph, then the lines of this equation will intersect each other at some point.

In this condition, we can conclude

- We get an intersecting line.
- Such a type of pair of linear equations with two variables where `a_1/a_2` is not equal to `b_1/b_2` have only one solution, i.e. unique solution.
- This type of equation is called a Consistent equation.

(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 these equations, the lines will coincide.

Thus, the conclusion in this condition is

- We get Consistent lines.
- Such a type of pair of linear equations with two variables where `a_1/a_2=b_1/b_2=c_1/c_2` have infinitely many solutions.
- This equation is also called a Consistent equation.

(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 parallel lines.

Here is the conclusion

- We will get parallel.
- Such a type of pair of linear equations with two variables where `a_1/a_2= b_1/b_2` is not equal to `c_1/c_2` have no solution.
- This type of Linear equation, which doesn't give any solution, is called an Inconsistent equation.

#### Video Tutorials

#### Shaalaa.com | Pair of Linear Equation in two variable part 2 (Graphical Method)

#### Related QuestionsVIEW ALL [41]

**Complete the following table to draw the graph of 2x – 6y = 3:**

x | −5 | `square` |

y | `square` | 0 |

(x, y) | `square` | `square` |