The pair of linear equations x + 2y + 5 = 0 and -3x = 6y - 1 has (A) unique solution (B) exactly two solutions (C) infinitely many solutions (D) no solution

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/3/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2024: question 1

Set in the CBSE Class 10 board exam of 2024, paper 30/3/1, section A, question 1, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q1 · 1 mark · MCQPair of Linear Equations in Two Variables

The pair of linear equations $x + 2 y + 5 = 0$ and $- 3 x = 6 y - 1$ has

(A)unique solution
(B)exactly two solutions
(C)infinitely many solutions
(D)no solution

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/3/1.

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: $x + 2 y + 5 = 0$ and $3 x + 6 y - 1 = 0$ .
Compare the ratios: $\frac{a _{1}}{a _{2}} = \frac{1}{3}$ , $\frac{b _{1}}{b _{2}} = \frac{2}{6} = \frac{1}{3}$ , $\frac{c _{1}}{c _{2}} = \frac{5}{- 1} = - 5$ .
Since $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$ , the lines are parallel. The pair has no solution, so the answer is option (D).
1 mark

Answer: No solution, option (D)

Where the marks are

Identifies that the pair has no solution, option (D) (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 30/3/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2024: question 1

Hints

Step-by-step solution

Revise the chapter

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