MathsCBSE Class 10 · Standard · Board exam 2023, set 30/2/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2023: question 30(b)

Set in the CBSE Class 10 board exam of 2023, paper 30/2/1, section C, question 30(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q30(b) · 3 marks · Short answerPair of Linear Equations in Two Variables

If $217 x + 131 y = 913$ and $131 x + 217 y = 827$ , then solve the equations for the values of $x$ and $y$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/2/1.

Hints

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

Hint 1

Notice the coefficients are swapped; try adding and subtracting the equations.

Hint 2

You will get simple equations for $x + y$ and $x - y$ .

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.

Adding the two equations: $348 x + 348 y = 1740 \Rightarrow x + y = 5$ …(i)
1 mark
Subtracting the second from the first: $86 x - 86 y = 86 \Rightarrow x - y = 1$ …(ii)
1 mark
Adding (i) and (ii): $2 x = 6 \Rightarrow x = 3$ ; then $y = 5 - 3 = 2$ .
1 mark

Answer: $x = 3$ , $y = 2$

Where the marks are

Adds the equations to get $x + y = 5$ (1 mark)
Subtracts to get $x - y = 1$ (1 mark)
Finds $x = 3$ , $y = 2$ (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: Elimination Method

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 30/2/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard 2023: question 30(b)

Hints

Step-by-step solution

Revise the chapter

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