MathsCBSE Class 10 · Basic · Sample paper, session 2023-24 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic sample paper 2023-24: question 21

From the official CBSE sample question paper for 2023-24, section B, question 21, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21 · 2 marks · Very short answerPair of Linear Equations in Two Variables

Find whether the following pair of linear equations is consistent or inconsistent:
$3 x + 2 y = 8$
$6 x - 4 y = 9$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

Write both equations in the form $a x + b y = c$ and list the coefficients.

Hint 2

Compare $\frac{a _{1}}{a _{2}}$ with $\frac{b _{1}}{b _{2}}$ . What does it mean when these two ratios are unequal?

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 each equation with $a x + b y = c$ :
$a_{1} = 3, b_{1} = 2, c_{1} = 8$ and $a_{2} = 6, b_{2} = - 4, c_{2} = 9$
1 mark
Ratios: $\frac{a _{1}}{a _{2}} = \frac{3}{6} = \frac{1}{2}$ , $\frac{b _{1}}{b _{2}} = \frac{2}{- 4} = - \frac{1}{2}$ , $\frac{c _{1}}{c _{2}} = \frac{8}{9}$
½ mark
Since $\frac{a _{1}}{a _{2}} \neq = \frac{b _{1}}{b _{2}}$ , the lines intersect at exactly one point. The pair has a unique solution, so it is consistent.
½ mark

Answer: Consistent (unique solution), since $\frac{a _{1}}{a _{2}} \neq = \frac{b _{1}}{b _{2}}$

Where the marks are

Identifies $a_{1}, b_{1}, c_{1}, a_{2}, b_{2}, c_{2}$ correctly (1 mark)
Computes the three ratios (1/2 mark)
Uses $\frac{a _{1}}{a _{2}} \neq = \frac{b _{1}}{b _{2}}$ to conclude the pair is consistent (1/2 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 paperSample paper 2023-24 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2023-24: question 21

Hints

Step-by-step solution

Revise the chapter

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