Assertion (A): The system of linear equations 3x + 5y - 4 = 0 and 15x + 25y - 25 = 0 is inconsistent. Reason (R): The pair of linear equations a_1x + b_1y + c_1 = 0 and a_2x + b_2y + c_2 = 0 is inconsistent if (a_1)/(a_2) = (b_1)/(b_2) ≠ (c_1)/(c_2). Directions: Choose the correct option. (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A). (B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A). (C) Assertion (A) is true, but Reason (R) is false. (D) Assertion (A) is false, but Reason (R) is true.

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/1/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Basic 2023: question 20

Set in the CBSE Class 10 board exam of 2023, paper 430/1/1, section A, question 20, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q20 · 1 mark · Assertion-reasonCompetency-basedPair of Linear Equations in Two Variables

Assertion (A): The system of linear equations $3 x + 5 y - 4 = 0$ and $15 x + 25 y - 25 = 0$ is inconsistent.

Reason (R): The pair of linear equations $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ is inconsistent if $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$ .

Directions: Choose the correct option.

(A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B)Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C)Assertion (A) is true, but Reason (R) is false.
(D)Assertion (A) is false, but Reason (R) is true.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/1/1.

Hints

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

Hint 1

Find the three ratios $a_{1} / a_{2}$ , $b_{1} / b_{2}$ , $c_{1} / c_{2}$ .

Hint 2

Which condition do they satisfy?

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.

$\frac{a _{1}}{a _{2}} = \frac{3}{15} = \frac{1}{5}$ , $\frac{b _{1}}{b _{2}} = \frac{5}{25} = \frac{1}{5}$ , $\frac{c _{1}}{c _{2}} = \frac{- 4}{- 25} = \frac{4}{25}$ .
$\frac{1}{5} = \frac{1}{5} \neq = \frac{4}{25}$ , so the system is inconsistent; A is true and R is the condition used. Option (A).
1 mark

Answer: Option (A)

Where the marks are

Compares ratios to show inconsistency explained by R (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 paper2023 board paper, set 430/1/1 (Basic): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Basic 2023: question 20

Hints

Step-by-step solution

Revise the chapter

More questions from Pair of Linear Equations in Two Variables