CBSE Class 10 Mathematics Pair of Linear Equation In Two Variables Worksheet Set E

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Chapter 3 Linear Equations Mathematics Worksheet for Class 10

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Class 10 Mathematics Chapter 3 Linear Equations Worksheet Pdf

CASE STUDY 1: An alumni association is an association of former students. These associations often organize social events, publish newsletters or magazines and raise funds for the organisation.The alumni meet of two batches of a college- batch A & batch B were held on the same day in the same hotel in two separate halls “Rose” and “Jasmine”. The rents were the same for both the halls. The expense for each hall is equal to the fixed rent of each hall and proportional to the number of persons attending each meet. 50 persons attended the meet in “Rose” hall, and the organisers had to pay ₹ 10000 towards the hotel charges. 25 guests attended the meet in “Jasmine” hall and the organisers had to pay ₹ 7500 towards the hotel charges. Denote the fixed rent by ₹ x and proportional expense per person by ₹ y.

Question. Represent algebraically the situation in hall “Rose”.
a) 50𝑥+𝑦=10000
b) 50𝑥−𝑦=10000
c) 𝑥+50𝑦=10000
d) 𝑥−50𝑦=10000
Answer : C

Question. Represent algebraically the situation in hall “Jasmine”
a) 𝑥+25𝑦=7500
b) 𝑥−25𝑦=7500
c) 25𝑥+𝑦=7500
d) 25𝑥−𝑦=7500
Answer : A

Question. What is the fixed rent of the halls?
a) ₹2500
b) ₹3300
c) ₹ 4000
d) ₹5000
Answer : D

Question. Find the amount the hotel charged per person.
a) ₹ 150
b) ₹ 190
c) ₹130
d) ₹ 100
Answer : D

 

Very Short Answer type Questions

Question. Find the value of (𝑥 + 𝑦)𝑖𝑓 ,3𝑥 − 2𝑦 = 5 𝑎𝑛𝑑 3𝑦 − 2𝑥 = 3
Answer : x + y = 8

Question. Solve for 𝑥 𝑎𝑛𝑑 𝑦 : 99𝑥 + 101 𝑦 = 499,101𝑥 + 99 𝑦 = 501
Answer : intersecting

Question. How many solutions do the equations 𝑦 = 0,𝑦 = − 7 posses?
Answer : 
X + y = 3, x – y =1

Question. Do the equations 𝑦 = 𝑥 𝑎𝑛𝑑 𝑦 = 𝑥 + 3 represent parallel lines?
Answer : Yes

Question. The value of k for which the equations 𝑘𝑥 + 𝑦 = 6 𝑎𝑛𝑑 6𝑥 + 2𝑦 = 12 will have infinitely many solutions is
Answer : y = 11− 3𝑋 / 5

Question. Express ‘x’ in terms of y of the equation 3x-y = 2 also check whether (-1,3) satisfies the equation or not?
Answer : 
9 & 6

Question. The sum of the digits of a two-digit number is 9. If 27 is added to it the number gets reversed. The number is
Answer : 
K = 2

Question. In how many points do the lines represented by the equations 𝑥 − 𝑦 = 0 𝑎𝑛𝑑 𝑥 + 𝑦 = 0 intersect?
Answer : one

Question. If 𝑥 = 𝑎 ,𝑦 = 𝑏 is the solutions of the equations 𝑥 − 𝑦 = 2 𝑎𝑛𝑑 𝑥 + 𝑦 = 4 find a &b.
Answer : 
36

Question. Find whether the lines representing the following pair of linear equations are intersecting, parallel or coinciding. 2𝑥 − 3𝑦 + 6 = 0; 4𝑥 − 5𝑦 + 2 = 0
Answer : K = 3

 

Short Answer type Questions

Question. The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the number. Find the number.
Answer : Let the ten’s and the unit’s digits in the number be x and y, respectively. So, the number may be written as 10x + y.
When the digits are reversed, x becomes the unit’s digit and y becomes the ten’s digit.
The number can be written as 10y + x.
According to the given condition,
x + y = 9                  ....(1)
We are also given that nine times the number
i.e., 9(10x + y) is twice the numbers obtained by reversing the order of the number i.e.
2(10y + x).
∴ 9(10x + y) = 2 (10y + x)
=> 90x + 9y = 20y + 2x
=>  90x – 2x + 9y – 20y = 0
=>  88x – 11y = 0
=> 8x – y = 0              ....(2)
Adding (1) and (2), we get
9x = 9
=>  x = 1
Putting x = 1 in (1), we get
y = 9 – 1 = 8
Thus, the number is
10 × 1 + 8 = 10 + 8 = 18
 
Question. The area of a rectangle remains the same if the length is decreased by 7 dm and breadth is increased by 5 dm. The area remains unchanged if its length is increased by 7 dm and and breadth decreased by 3 dm. Find the dimensions of the rectangle.
Answer : Let the length and breadth of a rectangle be x and y units respectively. So, area = (xy) sq. units.
First Case : Length is decreased by 7 dm and breadth is increased by 5 dm.
According to the question,
xy = (x – 7) (y + 5)
=> xy = xy + 5x – 7y – 35
=> 5x – 7y – 35 = 0                  ....(1)
Second Case : Length is increased by 7 dm and breadth is decreased by 3 dm.
Here, area also remains same
so, we get
xy = (x + 7) (y – 3) = xy – 3x + 7y – 21
=> 3x – 7y + 21 = 0                ....(2)
So, the system of equations becomes
=> 5x – 7y – 35 = 0                 ....(3)
3x – 7y + 21 = 0 ....(4)
Subtracting equation (4) from (3), we get
2x – 56 = 0
=> 2x = 56
=> x = 28 dm
Substituting x = 28 in equation (3), we get
5 × 28 – 7y = 35
=> 7y = 105
=> y = 15 dm
Hence, length and breadth of the rectangle are 28 dm and 15 dm respectively.

Question. If sum of two positive numbers is 108 and the difference of these numbers is 8, then find the numbers.
Answer : 

𝑥 + 𝑦 = 108
𝑥 – 𝑦 = 8
2𝑥 = 116
𝑥 = 58
𝑦 = 50

Question. Find the value of k for which the pair of linear equations 𝑘𝑥 + 3𝑦 = 𝑘 – 2 𝑎𝑛𝑑 12𝑥 + 𝑘𝑦 = 𝑘 has no solution
Answer : 

𝑘/12 =3/𝑘
k2 = 36
k = ±6

Question. Solve the following pair of linear equations by substitution method:
i. 3𝑥 + 2𝑦 – 7 = 0
ii. 4𝑥 + 𝑦 – 6 = 0
Answer : 

x = 7−2𝑦/3
4 × 7−2𝑦/3+𝑦−6=0
28 – 8𝑦 + 3𝑦 – 18 = 0
−5𝑦 + 10 = 0
𝑦 = 2 & 𝑥 = 1

Question. For which value of a and b does the following pair of linear equations has infinite number of solutions?
i. 2𝑥 – 3𝑦 = 7
ii. 𝑎𝑥 + 3𝑦 = 𝑏
Answer : 
2/𝑎 = −1 = 7/𝑏
a= -2
b = -7

Question. Solve for x and y:
i. x/a + y/b = 2
ii. a/x – b/y = 𝑎2 − 𝑏2
Answer : 

bx+ ay = 2 ab
ax – by = a2 - b2
(1) ×a
ab x + a2 y = 2a2b (3)
(2) ×𝑏
abx – b2 y = a2b + b3 (4)
(3) – (4)
(a2 + b2) y = a2b + b3
y = b
Sub y = b in (1)
x = a

 
CBSE Class 10 Mathematics Pair of Linear Equation In Two Variables Worksheet Set E
 
CBSE Class 10 Mathematics Pair of Linear Equation In Two Variables Worksheet Set E 2

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Chapter 3 Linear Equations CBSE Class 10 Mathematics Worksheet

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