Example 1: Let us take the example given in Section 3.1. Akhila goes to a fair with ` 20 and wants to have rides on the Giant Wheel and play Hoopla. Represent this situation algebraically and graphically (geometrically).
Example 2: Romila went to a stationery shop and purchased 2 pencils and 3 erasers for Rs. 9. Her friend Sonali saw the new variety of pencils and erasers with Romila, and she also bought 4 pencils and 6 erasers of the same kind for Rs. 18. Represent this situation algebraically and graphically.
Example 3: Two rails are represented by the equations x + 2y – 4 = 0 and 2x + 4y – 12 = 0. Represent this situation geometrically.
Example 4: Check graphically whether the pair of equations
x + 3y = 6 and 2x – 3y = 12
is consistent. If so, solve them graphically.
Example 5: Graphically, find whether the following pair of equations has no solution, unique solution or infinitely many solutions:
5x – 8y + 1 = 0, 3x – 24/5 y + 3/5 = 0
Example 6: Champa went to a ‘Sale’ to purchase some pants and skirts. When her friends asked her how many of each she had bought, she answered, “The number of skirts is two less than twice the number of pants purchased. Also, the number of skirts is four less than four times the number of pants purchased”. Help her friends to find how many pants and skirts Champa bought.
Example 7: Solve the following pair of equations by substitution method: 7x – 15y = 2, x + 2y = 3
Example 8: Solve Q.1 of Exercise 3.1 by the method of substitution.
Example 9: Let us consider Example 2 in Section 3.3, i.e., the cost of 2 pencils and 3 erasers is Rs. 9 and the cost of 4 pencils and 6 erasers is `Rs.18. Find the cost of each pencil and each eraser.
Example 10: Let us consider the Example 3 of Section 3.2. Will the rails cross each other?
