The value of k for which the system of linear equations x/2 + y/3 = 5 and 2x + ky = 7 is inconsistent, is (A) 3/4 (B) 4/3 (C) 1/3 (D) 3

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/4/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2026: question 8

Set in the CBSE Class 10 board exam of 2026, paper 30/4/1, section A, question 8, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q8 · 1 mark · MCQPair of Linear Equations in Two Variables

The value of k for which the system of linear equations $\frac{x}{2} + \frac{y}{3} = 5$ and $2 x + k y = 7$ is inconsistent, is

(A) $\frac{3}{4}$
(B) $\frac{4}{3}$
(C) $\frac{1}{3}$
(D)3

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/4/1.

Hints

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

Hint 1

Inconsistent means parallel lines.

Hint 2

Set $a_{1} / a_{2} = b_{1} / b_{2}$ .

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.

Inconsistent: $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$ , i.e. $\frac{1/2}{2} = \frac{1/3}{k}$ .
$\frac{1}{4} = \frac{1}{3 k} \Rightarrow k = \frac{4}{3}$ ; and $\frac{1}{4} \neq = \frac{5}{7}$ , so the system is inconsistent.
1 mark

Answer: $k = \frac{4}{3}$ , option (B)

Where the marks are

Uses ratio condition to get $k = 4/3$ (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 paper2026 board paper, set 30/4/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 8

Hints

Step-by-step solution

Revise the chapter

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