Which out of the following type of straight lines will be represented by the system of equations 3x + 4y = 5 and 6x + 8y = 7 ? (A) Parallel (B) Intersecting (C) Coincident (D) Perpendicular to each other

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/5/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2024: question 4

Set in the CBSE Class 10 board exam of 2024, paper 30/5/1, section A, question 4, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q4 · 1 mark · MCQPair of Linear Equations in Two Variables

Which out of the following type of straight lines will be represented by the system of equations $3 x + 4 y = 5$ and $6 x + 8 y = 7$ ?

(A)Parallel
(B)Intersecting
(C)Coincident
(D)Perpendicular to each other

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/5/1.

Hints

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

Hint 1

Compare the ratios of coefficients.

Hint 2

Equal x,y ratios but different constant ratio means what?

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.

$\frac{a _{1}}{a _{2}} = \frac{3}{6} = \frac{1}{2}$ , $\frac{b _{1}}{b _{2}} = \frac{4}{8} = \frac{1}{2}$ , $\frac{c _{1}}{c _{2}} = \frac{5}{7}$ .
Since $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$ , lines are parallel, option (A).
1 mark

Answer: Parallel, option (A)

Where the marks are

Compares ratios and concludes parallel (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 paper2024 board paper, set 30/5/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2024: question 4

Hints

Step-by-step solution

Revise the chapter

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