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

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/4/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2023: question 7

Set in the CBSE Class 10 board exam of 2023, paper 430/4/1, 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 $x + 2 y + 5 = 0$ and $- 3 x - 6 y + 1 = 0$ has:

(A)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 2023 board paper, set 430/4/1.

Hints

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

Hint 1

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

Hint 2

When the first two ratios are equal but the third is different, what do the lines look like?

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.

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, so there is no solution. Answer: option (D).
1 mark

Answer: No solution, option (D)

Where the marks are

Compares ratios of coefficients and concludes no solution (1 mark)

Revise the chapter

Chapter: Pair of Linear Equations in Two Variables (notes, formulas, where marks are lost and every past question)
Topic: Conditions for Number of Solutions

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 430/4/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2023: question 7

Hints

Step-by-step solution

Revise the chapter

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