MathsCBSE Class 10 · Standard · Sample paper, session 2024-25 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard sample paper 2024-25: question 32(A)

From the official CBSE sample question paper for 2024-25, 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

Solve the following system of linear equations graphically: $x + 2 y = 3$ , $2 x - 3 y + 8 = 0$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

For each equation, find at least two or three points by choosing values of $x$ .

Hint 2

Plot both lines on the same graph paper. The solution is the point where they meet; try $x = - 1$ in both tables.

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: $x + 2 y = 3 \Rightarrow y = \frac{3 - x}{2}$ .
Table: $x = 3, y = 0$ ; $x = 1, y = 1$ ; $x = - 1, y = 2$ .
Plot $(3, 0)$ , $(1, 1)$ , $(- 1, 2)$ and join them to get the line for $x + 2 y = 3$ .
2 marks
Line 2: $2 x - 3 y + 8 = 0 \Rightarrow y = \frac{2 x + 8}{3}$ .
Table: $x = - 4, y = 0$ ; $x = - 1, y = 2$ ; $x = 2, y = 4$ .
Plot $(- 4, 0)$ , $(- 1, 2)$ , $(2, 4)$ on the same axes and join them.
2 marks
The two lines intersect at $(- 1, 2)$ .
Check: $- 1 + 2 (2) = 3$ ✓ and $2 (- 1) - 3 (2) + 8 = 0$ ✓.
So the solution is $x = - 1$ , $y = 2$ .
1 mark

Answer: $x = - 1, y = 2$

Where the marks are

Makes a correct table and draws the line for $x + 2 y = 3$ (2 marks)
Makes a correct table and draws the line for $2 x - 3 y + 8 = 0$ (2 marks)
Reads the intersection point, $x = - 1$ , $y = 2$ (1 mark)

Revise the chapter

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

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 paperSample paper 2024-25 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard sample paper 2024-25: question 32(A)

Hints

Step-by-step solution

Revise the chapter

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