The pair of linear equations x + 2y - 5 = 0 and 2x - 4y + 6 = 0: (A) is inconsistent (B) is consistent with many solutions (C) is consistent with a unique solution (D) is consistent with two solutions

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/2/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2023: question 13

Set in the CBSE Class 10 board exam of 2023, paper 430/2/1, section A, question 13, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q13 · 1 mark · MCQPair of Linear Equations in Two Variables

The pair of linear equations $x + 2 y - 5 = 0$ and $2 x - 4 y + 6 = 0$ :

(A)is inconsistent
(B)is consistent with many solutions
(C)is consistent with a unique solution
(D)is consistent with two solutions

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/2/1.

Hints

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

Hint 1

Compare $a_{1} / a_{2}$ with $b_{1} / b_{2}$ .

Hint 2

Unequal ratios mean intersecting lines.

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.

$\frac{a _{1}}{a _{2}} = \frac{1}{2}$ , $\frac{b _{1}}{b _{2}} = \frac{2}{- 4} = - \frac{1}{2}$ .
Since $\frac{a _{1}}{a _{2}} \neq = \frac{b _{1}}{b _{2}}$ , the lines intersect: consistent with a unique solution. Option (C).
1 mark

Answer: Consistent with a unique solution, option (C)

Where the marks are

Compares ratios, $\frac{a _{1}}{a _{2}} \neq = \frac{b _{1}}{b _{2}}$ ⇒ unique solution (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 430/2/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2023: question 13

Hints

Step-by-step solution

Revise the chapter

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