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UNIT TEST

Unit test · Ch 3: Pair of Linear Equations in Two Variables

20marks
11questions
60%to pass
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Series RTEQ.P. Code 86/-2/0
Roll No.

RTE LEARN · CBSE PATTERN 2026–27

MATHEMATICS

Unit test · Ch 3: Pair of Linear Equations in Two Variables

Time allowed : 40 MinutesMaximum Marks : 20

General Instructions :

Read the following instructions carefully and follow them :

(i)This question paper contains 11 questions. All questions are compulsory.
(ii)This question paper is divided into three sections – A, B and C.
(iii)In Section A, Question numbers 1 to 5 carry 1 mark each.
(iv)In Section B, Question numbers 6 to 8 are very short answer (VSA) type questions carrying 02 marks each.
(v)In Section C, Question numbers 9 to 11 are short answer (SA) type questions carrying 03 marks each.
(vi)Draw neat figures wherever required. Take π = 22/7 wherever required, if not stated.
(vii)Use of calculators is not allowed.

SECTION A

This section comprises 5 questions of 1 mark each.

1.
State the condition on the coefficients for the pair a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 to have a unique solution.
1
2.
Find the point where the lines x + y = 8 and x − y = 2 intersect.
1
3.
Is x = 1, y = 2 a solution of the pair 3x − y = 1 and x + y = 3? Answer yes or no.
1
4.
How many solutions does a pair of linear equations have if a1/a2 = b1/b2 = c1/c2?
1
5.
The graphs of the pair 2x + 3y = 5 and 4x + 6y = 12 are intersecting, parallel or coincident? State which.
1

SECTION B

This section comprises 3 very short answer (VSA) type questions of 2 marks each.

6.
The sum of two numbers is 35 and their difference is 9. Find the numbers.
2
7.
Solve by the substitution method: x + 2y = 7 and 3x − y = 7.
2
8.
Find the value of k for which the pair 3x + 2y = 7 and 6x + ky = 9 has no solution.
2

SECTION C

This section comprises 3 short answer (SA) type questions of 3 marks each.

9.
The taxi charge for 6 km is ₹114 and for 10 km is ₹170. Taking a fixed charge ₹x and ₹y per km, find x and y and the charge for 15 km.
3
10.
The sum of the digits of a two-digit number is 11. If the digits are reversed, the number increases by 27. Find the number.
3
11.
Solve by the elimination method: 3x + 4y = 18 and 5x − 2y = 4.
3

✦ ✦ ✦

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Q6 · 2/2Full marks. Correct method and the final answer is clearly stated.
Q7 · 1/2Right approach, but one step of working is missing. Show every step to get full marks.
Q8 · 2/2Well explained, with correct units and a neat diagram.
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