**Case study Questions in the Class 10 Mathematics Chapter 3 **are very important to solve for your exam. Class 10 Maths Chapter 3 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving case study-based** **questions for Class 10 Maths Chapter 3 **Pair of Linear Equations in Two Variables**

In CBSE Class 10 Maths Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

# Pair of Linear Equations in Two Variables Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 10 Maths **Chapter 3 Pair of Linear Equations in Two Variables**

**Case Study/Passage-Based Questions**

**Case Study 1:** From the Bengaluru bus stand, if Riddhima buys 2 tickets to Malleswaram and 3 tickets to Yeswanthpur, then the total cost is Rs 46; but if she buys 3 tickets to Malleswaram and 5 tickets to Yeswanthpur, then the total cost is Rs 74.

Consider the fares from Bengaluru to Malleswaram and that to Yeswanthpur as Rs x and Rs y respectively and answer the following questions.

**(i) 1 ^{st} situation can be represented algebraically as**

(a) 3x-5y=74 | (b) 2x+5y=74 | (c) 2x-3y=46 | (d) 2x+3y=46 |

Answer: (d) 2x+3y=46

**(ii) 2 ^{nd} situation can be represented algebraically as**

(a) 5x + 3y = 74 | (b) 5x- 3y= 74 | (c) 3x + 5y = 74 | (d) 3x-5y=74 |

Answer: (c) 3x + 5y = 74

**(iii), Fare from Ben~aluru to Malleswaram is**

(a) Rs 6 | (b) Rs 8 | (c) Rs 10 | (d) Rs 2 |

Answer: (b) Rs 8

**(iv) Fare from Bengaluru to Yeswanthpur is**

(a) Rs 10 | (b) Rs 12 | (c) Rs 14 | (d) Rs 16 |

Answer: (a) Rs 10

**(v) The system oflinear equations represented by both situations has**

(a) infinitely many solutions | (b) no solution |

(c) unique solution | (d) none of these |

Answer: (c) unique solution

**Case Study 2:** The scissors which are so common in our daily life use, its blades represent the graph of linear equations.

Let the blades of a scissor are represented by the system of linear equations:

x + 3y = 6 and 2x – 3y = 12

**(i) The pivot point (point of intersection) of the blades represented by the linear equation x + 3y = 6 and 2x – 3y = 12 of the scissor is**(a) (2, 3)

(b) (6, 0)

(c) (3, 2)

(d) (2, 6)

Answer: (b) (6, 0)

**(ii) The points at which linear equations x + 3y = 6 and 2x – 3y = 12 intersect y – axis respectively are**(a) (0, 2) and (0, 6)

(b) (0, 2) and (6, 0)

(c) (0, 2) and (0, –4)

(d) (2, 0) and (0, –4)

Answer: (c) (0, 2) and (0, –4)

**(iii) The number of solution of the system of linear equations x + 2y – 8 = 0 and 2x + 4y = 16 is**(a) 0

(b) 1

(c) 2

(d) infinitely many

Answer: (d) infinitely many

**(iv) If (1, 2) is the solution of linear equations ax + y = 3 and 2x + by = 12, then values of a and b are respectively**(a) 1, 5

(b) 2, 3

(c) –1, 5

(d) 3, 5

Answer: (a) 1, 5

**(v) If a pair of linear equations in two variables is consistent, then the lines represented by two equations are**(a) intersecting

(b) parallel

(c) always coincident

(d) intersecting or coincident

Answer: (d) intersecting or coincident

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