MathsCBSE Class 10 · Standard · Board exam 2025, set 30/6/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2025: question 28

Set in the CBSE Class 10 board exam of 2025, paper 30/6/1, section C, question 28, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28 · 3 marks · Short answerPair of Linear Equations in Two Variables

Check whether the following pair of equations is consistent or not. If consistent, solve graphically

$x + 3 y = 6$

$3 y - 2 x = - 12$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/6/1.

Hints

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

Hint 1

Compare $a_{1} / a_{2}$ with $b_{1} / b_{2}$ to decide consistency.

Hint 2

Find points where each line cuts the axes and plot; see where the lines 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.

Write as $x + 3 y = 6$ and $- 2 x + 3 y = - 12$ . Then $\frac{a _{1}}{a _{2}} = \frac{1}{- 2}$ , $\frac{b _{1}}{b _{2}} = \frac{3}{3} = 1$ .
½ mark
Since $\frac{a _{1}}{a _{2}} \neq = \frac{b _{1}}{b _{2}}$ , the lines intersect at one point, so the pair is consistent (unique solution).
½ mark
Tables: $x + 3 y = 6$ : (0, 2), (3, 1), (6, 0). $- 2 x + 3 y = - 12$ : (0, −4), (3, −2), (6, 0). Plot these points on graph paper and draw both lines; they meet at (6, 0) on the x-axis.
1½ marks
Solution: $x = 6, y = 0$ .
½ mark

Answer: Consistent; $x = 6$ , $y = 0$

Where the marks are

Compares ratios $a_{1} / a_{2}$ and $b_{1} / b_{2}$ (½ mark)
Concludes consistent (½ mark)
Correct graph of both lines (1½ marks)
Reads solution (6, 0) (½ 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 paper2025 board paper, set 30/6/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 28

Hints

Step-by-step solution

Revise the chapter

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