MathsCBSE Class 10 · Basic · Board exam 2023, set 430/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2023: question 28(B)

Set in the CBSE Class 10 board exam of 2023, paper 430/4/1, section C, question 28(B), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28(B) · 3 marks · Short answerPair of Linear Equations in Two Variables

Find the values of ' $a$ ' and ' $b$ ' for which the system of linear equations $3 x + 4 y = 12$ , $(a + b) x + 2 (a - b) y = 24$ has infinite number of solutions.

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

Recall the ratio condition for coincident lines.

Hint 2

Each ratio must equal $\frac{12}{24} = \frac{1}{2}$ ; this gives two equations in a and b.

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.

For infinitely many solutions, $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} = \frac{c _{1}}{c _{2}}$ : $\frac{3}{a + b} = \frac{4}{2 ( a - b )} = \frac{12}{24}$
1 mark
$\frac{3}{a + b} = \frac{1}{2} \Rightarrow a + b = 6$
½ mark
$\frac{4}{2 ( a - b )} = \frac{1}{2} \Rightarrow \frac{2}{a - b} = \frac{1}{2} \Rightarrow a - b = 4$
½ mark
Adding: $2 a = 10 \Rightarrow a = 5$ ; then $b = 6 - 5 = 1$
1 mark

Answer: a = 5, b = 1

Where the marks are

Writes condition $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} = \frac{c _{1}}{c _{2}}$ with values (1 mark)
Gets $a + b = 6$ (½ mark)
Gets $a - b = 4$ (½ mark)
Solves $a = 5$ , $b = 1$ (½ + ½ 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 28(B)

Hints

Step-by-step solution

Revise the chapter

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