Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev

Mathematics (Maths) Class 10

Class 10 : Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev

The document Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev is a part of the Class 10 Course Mathematics (Maths) Class 10.
All you need of Class 10 at this link: Class 10

Short Answer Type Questions
Ques 1: For what value of p, the pair of linear equations
px = 2y
2x - y + 5 = 0 has unique solution?
Sol: We have:
px = 2y
⇒ p - 2y = 0
2x = y + 5
⇒ 2x - y = - 5
Here, a1 = p, b1 = - 2,
c1 = 0
a= 2, b2 = - 1,
c2 = - 5
For a unique solution,
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
⇒ p ≠ 2 × 2
⇒ p ≠ 4

Ques 2: In a cyclic quadrilateral PQRS, ∠P = (2x + 4)°, ∠Q = (y + 3)°, ∠R = (2y + 10)° and ∠S = (4x - 5)°. Find its four angles.
Sol:
In a cyclic quadrilateral, the opposite angles are supplementary.
∴∠P + ∠R = 180°
⇒ (2x + 4)° + (2y + 10)° = 180°
⇒ 2x + 2y + 14 - 180 = 0
⇒ 2x + 2y - 166 = 0
⇒ x + y - 83 = 0  ...(1)
Also ∠Q + ∠S = 180°
∴ (y + 3)° + (4x - 5)° = 180°
⇒ y + 4x - 2 - 180 = 0
⇒ y + 4x - 182 = 0 ...(2)
From (1) and (2),
a1 = 1, b1 = 1, c1 = - 83
a2 = 4, b2 = 1, c2 = - 182
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
∴ ∠P = (2x + 4)° = [(2 × 33) + 4]° = 70°
∠Q = (y + 3)° = [50 + 3]° = 53°
∠R = (2y + 10)° = [2 × 50 + 10]° = 110°
∠S = (4x - 5)° = [4 × 33 - 5°] = 127°

Ques 3: Solve:
23x + 35y = 209
35x + 23y = 197
Sol: We have:
23x + 35y = 209   ...(1)
35x + 23y = 197    ...(2)
88x + 88y = 406 [Adding (1) and (2)]
⇒ x + y = 7 ...(3) [Dividing by 88]
Subtracting (1) from (2),
35x + 23y = 197
23x + 35y = 209
(-) (-) (-)
12x - 12y = - 12
⇒ x - y = 1 ...(4) [Dividing by 12]
Adding (3) and (4),
2x = 8 ⇒ x = 4
From (3) x + y = 7 ⇒ 4 + y = 7
⇒ y = 3
So, x = 4 and y = 3.

Ques 4: Solve:
3x + 5y = 70   ...(1)
7x - 3y = 60   ...(2)
Sol: From (1) and (2), we have:
a1 = 3, b1 = 5, c1 = - 70
a2 = 7, b2 = - 3, c2 = - 60
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Thus, the required solution is:
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev .

Ques 5: Without drawing the graphs, state whether the following pair of linear equations will represent intersecting lines, coinciding lines or parallel lines:
6x - 3y + 10 = 0
2x - y + 9 = 0
Sol: Here, the given set of equations is:
6x - 3y + 10 = 0   ...(1)
2x - y + 9 = 0    ...(2)
From (1) and (2), we have:
a1 = 6, b1 = - 3, c1 = 10
a2 = 2, b2 = - 1, c2 = 9
Now, Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
∴We have
= Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
This condition represents parallel lines. Hence, the given pair represents parallel lines.

Ques 6: Check graphically whether the pair of equations 
3x - 2y + 2 = 0
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev= 0 
is consistent. Also find the co-ordinates of the points where the graphs of the equations meet the y-axis.
Sol: ∴ 3x - 2y + 2 = 0 ⇒ y = Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev ..(1)
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Also = 0 ⇒ y = Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev ...(2)
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Plotting the points (0, 1), (2, 4), (- 2, - 2) and (0, 3), (2, 6), (–2, 0) we get two straight lines l1 and l2 which are parallel.
∴ The given equations are inconsistent.
From the graph we observe that line l1 meets the y-axis at (0, 1) and the line l2 meets the y-axis at (0, 3).
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev

Ques 7: A fraction becomes, if 2 is added to both numerator and denominator. If 3 is added to both numerator and denominator, it becomes 2/5. Find the fraction.
Sol: Let the fraction be x/y.
From 1st condition,
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev

⇒ 3x + 6 = y + 2
⇒ 3x − y + 4 = 0 ...(1)
From 2nd conditon,
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev

⇒ 5x + 15 = 2y + 6
⇒ 5x − 2y + 9 = 0 ...(2)
From (1) and (2), we have:
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev

Ques 8: Check graphically whether the pair of equations
3x + 5y = 15
x - y = 5
is consistent. Also find the coordinates of the points where the graphs of equations meet the y-axis.
Sol: We have
3x + 5y = 15
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
And from x - y = 5
⇒ y = x - 5
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Plotting the above two sets of points we get two straight lines l1 and l2 which intersect at the point (5, 0).
Thus, the given system is consistent.
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Obviously the line l1 meets the y-axis at (0, 3) and line l2 meets the y-axis at (0, - 5).

Ques 9: Places A and B are 160 km apart on highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 8 hours, but if they travel towards each other, they meet in 2 hours. What are the speeds of the two cars? 
Sol: Let the car-I and car-II starts from A and B at x km/hr and y km/hr respectively.
Case-I: [Cars are moving in the same direction]
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Let the two cars meet at C after 8 hours.
Distance covered:
by car-I = AC = 8x km
by car-II = BC = 8y km
∴ AB = AC - BC
⇒ 160 = 8x - 8y
⇒ x - y = 20   ...(1)
Case-II: [Cars are moving in opposite directions]
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev

Let, after 2 hours, the cars meet at D.
∴ Distance cover after 2 hours,
by car-I = AD = 2x km
by car-II = BD = 2y km
⇒ AB = AD + BD
⇒ 160 = 2x + 2y
⇒ 80 = x + y
⇒ x + y = 80 ...(2)
Adding (1) and (2), we get
x + y = 80
x - y = 20
2x = 100
⇒ x = 100/2 = 50
⇒ Substituting x = 50 in (1), we get
x - y = 20 ⇒ 50 - y = 20
⇒ y = 50 - 20 = 30
⇒ Speed of car-I = 50 km/hr
Speed of car-II = 30 km/hr.

Ques 10: Solve for x and y:
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Sol: We have:
= Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev   ...(1)
ax − by = 2ab    ...(2)
Dividing (2) by a, we have:
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev   ...(3)
From (1) and (3), we have
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
From (2),
ab - by = 2ab
⇒ - by = 2ab - ab = ab
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
y = - a
Thus, x = b and y = - a.

Ques 11: The sum of two numbers is 8. Determine the numbers if the sum of their reciprocals is 8/15.
Sol: Let the two numbers be x and y.
According to the conditions:
x + y = 8 ...(1)
=Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev ..(2)
From (1), x = (8 - y)
Substituting x = (8 - y) in (2),
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
⇒ 8 × 15 = 8 × y (8 - y)
⇒ 64y - 8y2 - 120 = 0
⇒- y2 + 8y - 15 = 0
⇒ y2 - 8y + 15 = 0
⇒ y2 - 5y - 3y + 15 = 0
⇒ y (y - 5) - 3 (y - 5) = 0
⇒ (y - 5) (y - 3) = 0
⇒ If y - 5 = 0 then y = 5
or if y - 3 = 0, then y = 3
Since x = 8 - y
⇒ when y = 5,
then x = 8 - 5 = 3
when y = 3, then
x = 8 - 3 = 5
⇒ The required numbers are (3, 5) or
(5, 3).

Ques 12: Solve the following pair of equations:
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Sol: Let Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
⇒The given system of equations becomes:
5p + q = 2 ...(1)
6p - 3q = 1 ...(2)
Multiplying (1) by 3 and adding to (2),
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
and 5p + q = 2 ⇒ Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev

Since, Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
= 3 ⇒ x = 4
Also, Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
⇒ y - 2 = 3 ⇒ y = 5
Thus, x = 4 and y = 4
⇒ 3y - 6 = 1
⇒ 3y = 1 + 6 = 7
⇒ y = 7/3

Ques 13: Solve the following pair of equations:
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Sol: Let Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
⇒ The given pair of equation is expressed as
10p + 2q = 4 ⇒ 5p + q = 2   ...(1)
15p - 5q = - 2 ...(2)
Multiplying (1) by 5 and adding to (2)
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
From (1), Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
⇒1 + q = 2 ⇒ q = 2 - 1 = 1
Since, Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
⇒ x + y = 5   ...(3)
And Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
⇒ x − y = 1   ...(4)
Adding (3) and (4),
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
From (3), 3 + y = 5 ⇒ y = 2
Thus, x = 3 and y = 2.

Ques 14: Solve for x and y:
37x + 43y = 123
43x + 37y = 117
Sol: We have:
37x + 43y = 123 ...(1)
43x + 37y = 117 ...(2)
Adding (1) and (2)
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Dividing both sides by 80, we get
x + y = 3 ...(3)
Subtracting (2) from (1),
- 6x + 6y = 6 ⇒ - x + y = 1 ...(4)
Adding:
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
⇒ y = 4/2 = 2
Putting y = 2 in x + y = 3, we get
x + 2 = 3 ⇒ x = 3 - 2 = 1
Thus, x = 1 and y = 2.

Ques 15: Solve for ‘x’ and ‘y’:
(a - b) x + (a + b) y = a2 - 2ab - b2
(a + b) (x + y) = a2 + b2
Sol: We have:
(a - b) x + (a + b) y = a2 - 2ab - b2   ...(1)
(a + b) x + (a + b) y = a2 + b2   ...(2)
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
− 2b x = − 2ab − b
⇒ (− 2b) x = − 2b (a + b)
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
From (2),
(a + b) (a + b) + (a + b) y = a2 + b2
⇒(a + b)2 + (a + b) y = (a2 + b2)
⇒ (a + b) y = (a2 + b2) - (a + b)2
⇒ (a + b) y = a2 + b2 - (a2 + b2 + 2ab)
⇒ (a + b) y = a2 + b2 - a2 - b2 - 2ab
⇒ (a + b) y = - 2ab
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Thus, x = (a + b) and
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Ques 16: Represent the following pair of equations graphically and write the co-ordinates of points where the lines intersect y-axis:
x + 3y = 6, 2x - 3y = 12
Sol: We have:
x + 3y = 6
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev

and 2x - 3y = 12
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Plotting the above points, we get two straight lines l1 and l2 such that they intersect at (6, 0) as shown below:
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Obviously,
The line l1 meets the y-axis at (0, 2).
The line l2 meets the y-axis at (0, - 4).

Ques 17: Solve for x and y:
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Sol: Let Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
∴ We have:
5p + q = 2   ...(1)
6p - 3q = 1   ...(2)
From (1) and (2), we have:
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
And Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Now, Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
⇒ x − 1 = 3 ⇒ x = 4
And Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
⇒ y − 2 = 3 ⇒ y = 5
Thus x = 4 and y = 5

Ques 18: For what values of ‘a’ and ‘b’ does the following pair of equations have an infinite number of solutions?
2x + 3y = 7
a (x + y) - b (x - y) = 3a + b - 2
Sol: We have:
2x + 3y = 7   ...(1)
a (x + y) - b (x - y) = 3a + b - 2   ...(2)
From (2), we have:
a (x + y) - b (x - y) = 3a + b - 2
⇒ ax + ay - bx + by = 3a + b - 2
⇒ ax - bx + ay + by = 3a + b - 2
⇒ (a - b) x + (a + b) y = 3a + b - 2
Now, A1 = 2, B1= 3,
C1 = - 7
A2 = (a - b), B2
= (a + b),
C2 = - [3a + b - 2]
For infinite number of solutions,
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
i.e., Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev

⇒ 2 (a + b) = 3 (a − b)
⇒ 2a + 2b − 3a + 3b = 0
⇒ − a + 5b = 0
⇒ a = 5b ...(3)
Also = Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
⇒ 3 (3a + b - 2) = 7 (a + b)
⇒ 9a + 3b - 6 = 7a + 7b
⇒ 9a - 7a + 3b - 7b = 6
⇒ 2a - 4b = 6
⇒ a - 2b = 3    ...(4)
From (3) and (4),
5b - 2b = 3
⇒ 3b = 3 ⇒ b = 1
Thus, a = 5 × b
⇒ a = 5 × 1 = 5
i.e., a = 5 and b = 1.

Ques 19: Solve the following pairs of equations for x and y:
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Sol: Let Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
∴ We have:
15p + 22q = 5 ...(1)
40p + 55q = 13 ...(2)
From (1) and (2), we get
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Adding (3) and (4), we have
2x = 16 ⇒ x = 16/2 =8
From (4), 8 + y = 11 ⇒ y = 11 - 8 = 3
Thus, x = 8 and y = 3.

Ques 20: Draw the graph of the pair of linear equations x – y + 2 = 0 and 4x – y – 4 = 0. Calculate the area of triangle formed by the lines so drawn and x-axis.
Sol: 
To draw the graph of the given pair of equations, we have the table of ordered pairs
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Plot the points A(0, 2), B(–2, 0); C(0, –4) and D(1, 0) on the graph paper and join the points to form the lines AB and CD :
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
From the graph, we find that the points P(2, 4) is common to both the lines AB and CD.
These lines meet x-axis at B(–2, 0) and D(1, 0).
Thus, the triangle BDP is formed by the lines and the x-axis.
The vertices of this Δ are
B(–2, 0), D(1, 0)  and    P(2, 4)
Now, base of ΔBDP = BD
= (BO + OD)
= (2 + 1) units
= 3 units
Altitude of the ΔBDP = PQ
= 4 units
∴ Area of ΔBDP = Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
=  6 sq. units

Ques 21: It can take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter for 9 hours, only half the pool can be filled. How long would it take for each pipe to fill the pool separately?
Sol: Let the time taken by the pipe of larger diameter to fill the pool separately = x hours.
The time taken by the pipe of smaller diameter to fill the pool separately = y hours.
∴ Part of the pool fill by the pipe of larger diameter in 1 hour = 1/x.
Part of fool filled by the pipe of larger diameter in 4 hours = 4/x.
Similarly, Part of the pool filled by the pipe of smaller diameter in 9 hours = 9/y.
∴We have =  Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev...(1)
Since, the pool is fill by both the pipes together in 12 hours.
∴  Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev   ...(2)
To solve (1) and (2), multiplying (1) by 3 and subtracting (2) from it, we have
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Substituting, y = 30 in (2), we have
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev
⇒ x = 20
⇒ Required time taken by pipe of larger diameter = 20 hours

Required time taken by pipe of smaller diameter = 30 hours

Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Complete Syllabus of Class 10

Dynamic Test

Content Category

Related Searches

shortcuts and tricks

,

past year papers

,

Important questions

,

Viva Questions

,

Summary

,

Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev

,

mock tests for examination

,

pdf

,

Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev

,

video lectures

,

practice quizzes

,

Exam

,

Sample Paper

,

Short Answer Type Questions- Pair of Linear Equations in Two Variables Class 10 Notes | EduRev

,

Objective type Questions

,

Previous Year Questions with Solutions

,

Semester Notes

,

Extra Questions

,

Free

,

ppt

,

MCQs

,

study material

;