MathsCBSE Class 10 · Basic · Board exam 2023, set 430/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2023: question 24(b)

Set in the CBSE Class 10 board exam of 2023, paper 430/1/1, section B, question 24(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24(b) · 2 marks · Very short answerPair of Linear Equations in Two Variables

Find out whether the following pair of linear equations are consistent or inconsistent : $5 x - 3 y = 11$ , $- 10 x + 6 y = 22$ .

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

Hints

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

Hint 1

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

Hint 2

If the first two ratios are equal but the third differs, the lines are parallel.

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.

Here $a_{1} = 5, b_{1} = - 3, c_{1} = - 11$ and $a_{2} = - 10, b_{2} = 6, c_{2} = - 22$ . $\frac{a _{1}}{a _{2}} = \frac{5}{- 10} = - \frac{1}{2}$ , $\frac{b _{1}}{b _{2}} = \frac{- 3}{6} = - \frac{1}{2}$ , $\frac{c _{1}}{c _{2}} = \frac{- 11}{- 22} = \frac{1}{2}$ .
1 mark
So $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$ .
½ mark
Hence the lines are parallel and the pair of equations is inconsistent.
½ mark

Answer: Inconsistent

Where the marks are

Computes the three ratios correctly (1 mark)
Shows $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$ (½ mark)
Concludes the pair is inconsistent (½ 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 paper2023 board paper, set 430/1/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2023: question 24(b)

Hints

Step-by-step solution

Revise the chapter

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