MathsCBSE Class 10 · Standard · Board exam 2024, set 30/2/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2024: question 32(a)

Set in the CBSE Class 10 board exam of 2024, paper 30/2/1, section D, question 32(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32(a) · 5 marks · Long answerPair of Linear Equations in Two Variables

Using graphical method, solve the following system of equations: $3 x + y + 4 = 0$ and $3 x - y + 2 = 0$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/2/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Write each equation as $y$ in terms of $x$ and make a table of at least two or three points.

Hint 2

Plot both lines on the same axes; the solution is where they meet.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Line 1: $3 x + y + 4 = 0 \Rightarrow y = - 3 x - 4$ . Table: $x = 0, - 1, - 2$ give $y = - 4, - 1, 2$ . Plot $(0, - 4), (- 1, - 1), (- 2, 2)$ on graph paper and join them to get a straight line.
2 marks
Line 2: $3 x - y + 2 = 0 \Rightarrow y = 3 x + 2$ . Table: $x = 0, - 1, 1$ give $y = 2, - 1, 5$ . Plot $(0, 2), (- 1, - 1), (1, 5)$ and join them to get the second straight line.
2 marks
The two lines intersect at $(- 1, - 1)$ . Hence the solution is $x = - 1, y = - 1$ . (Check: $3 (- 1) + (- 1) + 4 = 0$ and $3 (- 1) - (- 1) + 2 = 0$ .)
1 mark

Answer: $x = - 1$ , $y = - 1$

Where the marks are

Correct table and correctly drawn line for $3 x + y + 4 = 0$ (2 marks)
Correct table and correctly drawn line for $3 x - y + 2 = 0$ (2 marks)
Reads intersection point: $x = - 1, y = - 1$ (1 mark)

Revise the chapter

Chapter: Pair of Linear Equations in Two Variables (notes, formulas, where marks are lost and every past question)
Topic: Graphical Method of Solving Linear Equations

Practise this chapterBoard-style questions from Pair of Linear Equations in Two Variables, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 30/2/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2024: question 32(a)

Hints

Step-by-step solution

Revise the chapter

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