Case Study Questions for Class 9 Maths Chapter 4 Linear Equations in Two Variables

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Looking for high-quality practice material for your math exams? You’re in the right place. Below, we are providing important Case Study Questions for CBSE Class 9 Maths Chapter 4 Linear Equations in Two Variables. These passage-based questions are perfectly aligned with the latest syllabus to help you practice competency-based learning. Read through the real-world scenario of buying vegetables, test your ability to form and graph linear equations, and verify your steps using our detailed explanations!

Case Study Questions for Class 9 Maths Chapter 4 Linear Equations in Two Variables

1 Case Studies · 4 Questions · With Answer & Explanation

1

Case Study: Linear Equations in Daily Life

Read the passage carefully, then answer all five questions
Linear Equations in Two Variables

Anil went to buy some vegetables. He bought ‘x’ kg of tomatoes and ‘y’ kg of potatoes. The total cost of the vegetables comes out to be Rs. 200. The cost of 1 kg of tomatoes is Rs. 50 and the cost of 1 kg of potatoes is Rs. 20.

i
Which of the following equations represents the total cost?
a 5x – 2y = 20
b 5y + 2x = 20
c 5x + 2y = 20
d 2x + 5y = 20
Correct Answer (c) 5x + 2y = 20 ✅
Explanation

The cost of $x$ kg of tomatoes is $50x$, and the cost of $y$ kg of potatoes is $20y$. The total cost is Rs. 200. Setting up the equation:

$$50x + 20y = 200$$

Dividing the entire equation by 10 gives:

$$5x + 2y = 20$$
ii
If Anil bought ‘x’ kg of tomatoes and 2.5 kg of potatoes, then find the value of ‘x’.
a 5
b 2
c 3
d 4
Correct Answer (c) 3 ✅
Explanation

Substitute $y = 2.5$ into the cost equation:

$$50x + 20(2.5) = 200$$
$$50x + 50 = 200$$

Subtract 50 from both sides:

$$50x = 150 \implies x = 3$$
iii
If Anil bought 2 kg of tomatoes and ‘y’ kg of potatoes, then find the value of ‘y’.
a 5
b 2
c 3
d 4
Correct Answer (a) 5 ✅
Explanation

Substitute $x = 2$ into the cost equation:

$$50(2) + 20y = 200$$
$$100 + 20y = 200$$

Subtract 100 from both sides:

$$20y = 100 \implies y = 5$$
iv
The graph of 5x + 2y = 20 cuts the x-axis at the point:
a (10, 0)
b (4, 0)
c (0, 0)
d it is parallel to x-axis
Correct Answer (b) (4, 0) ✅
Explanation

To find where the graph cuts the x-axis, substitute $y = 0$ into the simplified equation:

$$5x + 2(0) = 20$$
$$5x = 20 \implies x = 4$$

Therefore, the point of intersection is $(4, 0)$.

v
The graph of 5x + 2y = 20 cuts the y-axis at the point:
a (0, 10)
b (0, 4)
c (0, 0)
d it is parallel to y-axis
Correct Answer (a) (0, 10) ✅
Explanation

To find where the graph cuts the y-axis, substitute $x = 0$ into the simplified equation:

$$5(0) + 2y = 20$$
$$2y = 20 \implies y = 10$$

Therefore, the point of intersection is $(0, 10)$.

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