Answer the following. (a) Solve the following pair of linear equations by graphical method: 2x + y = 9 and x - 2y = 2. (b) Nidhi received simple interest of ₹ 1,200 when invested ₹ x at 6% p.a. and ₹ y at 5% p.a. for 1 year. Had she invested ₹ x at 3% p.a. and ₹ y at 8% p.a. for that year, she would have received simple interest of ₹ 1,260. Find the values of x and y.

MathsCBSE Class 10 · Basic · Board exam 2025, set 430/6/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2025: question 32(a)

Set in the CBSE Class 10 board exam of 2025, paper 430/6/1, section D, question 32(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32(a) · 5 marks · Long answerCompetency-basedPair of Linear Equations in Two Variables

Answer the following.

(a)
Solve the following pair of linear equations by graphical method: $2 x + y = 9$ and $x - 2 y = 2$ .
0 marks
(b)
Nidhi received simple interest of ₹ 1,200 when invested ₹ $x$ at 6% p.a. and ₹ $y$ at 5% p.a. for 1 year. Had she invested ₹ $x$ at 3% p.a. and ₹ $y$ at 8% p.a. for that year, she would have received simple interest of ₹ 1,260. Find the values of $x$ and $y$ .
0 marks

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/6/1.

Hints

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

Hint 1

Make a table of at least three points for each equation by choosing values of x.

Hint 2

Plot both lines on the same axes; the solution is where they cross — look at x = 4.

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 $2 x + y = 9$ , i.e. $y = 9 - 2 x$ :
$x$ 0 2 4
$y$ 9 5 1
Plot (0, 9), (2, 5), (4, 1) on graph paper and join them to draw the line $2 x + y = 9$ .
2 marks
For $x - 2 y = 2$ , i.e. $y = \frac{x - 2}{2}$ :
$x$ 0 2 4
$y$ −1 0 1
Plot (0, −1), (2, 0), (4, 1) and join them to draw the line $x - 2 y = 2$ on the same axes.
2 marks
The two lines intersect at the point (4, 1). Hence the solution is $x = 4, y = 1$ .
(Check: $2 (4) + 1 = 9$ and $4 - 2 (1) = 2$ .)
1 mark

$x$	0	2	4
$y$	9	5	1

$x$	0	2	4
$y$	−1	0	1

Answer: $x = 4, y = 1$

Where the marks are

Correct table and graph of $2 x + y = 9$ (2 marks)
Correct table and graph of $x - 2 y = 2$ (2 marks)
Reads intersection point (4, 1) as 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 paper2025 board paper, set 430/6/1 (Basic): 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 Basic 2025: question 32(a)

Hints

Step-by-step solution

Revise the chapter

More questions from Pair of Linear Equations in Two Variables