The pair of linear equations 2x = 5y + 6 and 15y = 6x - 18 represents two lines which are: (A) intersecting (B) parallel (C) coincident (D) either intersecting or parallel

MathsCBSE Class 10 · Standard · Board exam 2023, set 30/4/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2023: question 7

Set in the CBSE Class 10 board exam of 2023, paper 30/4/1, section A, question 7, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q7 · 1 mark · MCQPair of Linear Equations in Two Variables

The pair of linear equations $2 x = 5 y + 6$ and $15 y = 6 x - 18$ represents two lines which are:

(A)intersecting
(B)parallel
(C)coincident
(D)either intersecting or parallel

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/4/1.

Hints

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

Hint 1

Bring both equations to the form $a x + b y + c = 0$ .

Hint 2

Compare $a_{1} / a_{2}$ , $b_{1} / b_{2}$ and $c_{1} / c_{2}$ .

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.

Write both equations in standard form: $2 x - 5 y - 6 = 0$ and $6 x - 15 y - 18 = 0$ .
Compare the coefficients: $\frac{a _{1}}{a _{2}} = \frac{2}{6} = \frac{1}{3}$ , $\frac{b _{1}}{b _{2}} = \frac{- 5}{- 15} = \frac{1}{3}$ , $\frac{c _{1}}{c _{2}} = \frac{- 6}{- 18} = \frac{1}{3}$ .
All three ratios are equal, so the lines are coincident. The answer is option (C).
1 mark

Answer: Coincident, option (C)

Where the marks are

Chooses option (C) coincident (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 paper2023 board paper, set 30/4/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2023: question 7

Hints

Step-by-step solution

Revise the chapter

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