The document discusses methods for solving linear equations in two variables: 1. Graphical methods involve finding the point of intersection between the graphs of the two linear equations. This intersection point provides the solution. 2. Algebraic methods include substitution and elimination techniques to solve for the variables algebraically. Examples are then provided to demonstrate solving word problems by setting up and solving the corresponding linear equations.

1. Solution Of Equations
LINEAR EQUATION IN TWO VARIABLES
1. Graphical Methods
2. Algebraic Methods For Solving Equations.
1. Substitution Methods
2. Elimination Methods

2. LINEAR EQUATION IN TWO VARIABLES
1. Graphical methods
The intersection point of the straight lines depicting the equations is the solution for equation.
𝑎1
𝑎2
≠
𝑏1
𝑏2
intersecting 𝑙𝑖𝑛𝑒 = Unique solution

3. POINT OF INTERSECTION

4. No solution
𝒂𝟏
𝒂𝟐
=
𝒃𝟏
𝒃𝟐
≠
𝒄𝟏
𝒄𝟐
𝒑𝒂𝒓𝒆𝒍𝒍𝒆𝒍 𝒍𝒊𝒏𝒆 = 𝐍𝐨 𝐬𝐨𝐥𝐮𝐭𝐢𝐨𝐧

5. INFINITE SOLUTION
𝒂𝟏
𝒂𝟐
=
𝒃𝟏
𝒃𝟐
=
𝒄𝟏
𝒄𝟐
𝒄𝒐𝒊𝒏𝒄𝒊𝒅𝒆𝒏𝒕 𝒍𝒊𝒏𝒆 = 𝐢𝐧𝐟𝐢𝐧𝐢𝐭𝐥𝐲 𝐦𝐚𝐧𝐲 𝐬𝐨𝐥𝐮𝐭𝐢𝐨𝐧

6. Q.1 The cricket coach in a school purchased 3 bats and 6 balls for Rs. 3900. He bought a
bat and two balls from the same shop for Rs. 1300.(C.G.Board)

7. Q.2The sum of two numbers is 16 and their difference is 8. (C.G.Board)

8. Q.3The cost of 2 kg apples and 1 kg grapes is Rs. 160 in a fruit shop. In the same shop,
the cost of 4 kg apples and 2 kg grapes is Rs. 300. (C.G.Board)

9. Q.4Naresh said to his daughter that seven years ago my age was seven times your age and
three years from now I will be three times as old as you. (C.G.Board)

10. Q.5 A person travels 90 km by train and taxi to reach his office. The distance travelled by
train is twice the distance travelled by taxi. (C.G.Board)

15. Q.1.10 students of Class X took part in a Mathematics quiz. If the number of girls is 4
more than the number of boys, find the number of boys and girls who took part in
the quiz.(CBSE.Board)

16. 5 pencils and 7 pens together cost 50, whereas 7 pencils and 5 pens together cost 46. Find
the cost of one pencil and that of one pen..(CBSE.Board)