Class X Math Chapter 3 NCERT Solutions

Exercise 3.1

Q1. Check whether (2, 1) is a solution of

x + y = 3

Substitute:
2 + 1 = 3 ✔

👉 Yes, it is a solution

অসমীয়া:
(2,1) সমাধান।

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Q2. Check whether (0, −1) is a solution of

2x + y = −1

2(0) − 1 = −1 ✔

👉 Yes

Q1.

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.

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✅ Step 1: Form the equations

Let
Number of boys = x
Number of girls = y

According to the question:

1. Total students = 10

$$x + y = 10$$x+y=10

2. Girls are 4 more than boys

$$y = x + 4$$y=x+4

or$$y – x = 4$$y−x=4

👉 Pair of linear equations:$$x + y = 10 \quad (1)$$x+y=10(1) $$y – x = 4 \quad (2)$$y−x=4(2)

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✅ Step 2: Solve graphically

Convert into graph-friendly form:

From (1):$$y = 10 – x$$y=10−x

From (2):$$y = x + 4$$y=x+4

Plot both equations on the graph.
The two lines intersect at point (3, 7).

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✅ Solution:

• Number of boys = 3
• Number of girls = 7

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অসমীয়া ব্যাখ্যা:

ধৰি লওঁ,
ল’ৰাৰ সংখ্যা = x
ছোৱালীৰ সংখ্যা = y

মুঠ শিক্ষাৰ্থী = 10

x+y=10

ছোৱালী ল’ৰাতকৈ 4 জন বেছি

y=x+4

গ্ৰাফ অঁকিলে ছেদন বিন্দু = (3, 7)

👉 ল’ৰা = 3 জন, ছোৱালী = 7 জন

Q2.

5 pencils and 7 pens together cost ₹50, whereas 7 pencils and 5 pens together cost ₹46. Find the cost of one pencil and one pen.

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✅ Step 1: Form the equations

Let
Cost of one pencil = x (₹)
Cost of one pen = y (₹)

Given:

1. 5 pencils + 7 pens cost ₹50

$$5x + 7y = 50$$5x+7y=50

2. 7 pencils + 5 pens cost ₹46

$$7x + 5y = 46$$7x+5y=46

👉 Pair of linear equations:$$5x + 7y = 50 \quad (1)$$5x+7y=50(1) $$7x + 5y = 46 \quad (2)$$7x+5y=46(2)

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✅ Step 2: Solve graphically

Convert into slope-intercept form:

From (1):$$7y = 50 – 5x \Rightarrow y = \frac{50 – 5x}{7}$$7y=50−5x⇒y=750−5x​

From (2):$$5y = 46 – 7x \Rightarrow y = \frac{46 – 7x}{5}$$5y=46−7x⇒y=546−7x​

Plot both straight lines on the same graph.
They intersect at point (4, 2).

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✅ Solution:

• Cost of one pencil = ₹4
• Cost of one pen = ₹2

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অসমীয়া ব্যাখ্যা:

এটা পেঞ্চিলৰ মূল্য = x টকা
এটা কলমৰ মূল্য = y টকা

5x+7y=50

7x+5y=46

গ্ৰাফ অঁকিলে ছেদন বিন্দু = (4, 2)

👉 পেঞ্চিল = ₹4, কলম = ₹2

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