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RD Sharma Test: Pair of Linear Equations in Two Variables - Class 10 MCQ


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25 Questions MCQ Test Mathematics (Maths) Class 10 - RD Sharma Test: Pair of Linear Equations in Two Variables

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RD Sharma Test: Pair of Linear Equations in Two Variables - Question 1

A system of two linear equations in two variables has infinitely many solutions, if their graphs

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 1

A system of two linear equations in two variables has infinitely many solutions, if their graphs coincide with each other

RD Sharma Test: Pair of Linear Equations in Two Variables - Question 2

The area of the triangle formed by the lines 2x + y = 6, 2x – y + 2 = 0 and the x – axis is

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 2

Here are the two solutions of each of the given equations. 2x+y = 6
2x+y=0


The area bounded by the given lines and x−axis has been shaded in the graph. 

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RD Sharma Test: Pair of Linear Equations in Two Variables - Question 3

The system of equations x – 4y = 8, 3x – 12y = 24

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 3

Given

Therefore, the system has infinite many solution.

RD Sharma Test: Pair of Linear Equations in Two Variables - Question 4

The system of linear equations a1x+b1y+c= 0 and a2x+b2y+c2 = 0 has a unique solution if

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 4

The system of linear equations a1x+b1y+c= 0 and a2x+b2y+c2 = 0 has a unique solution if 

RD Sharma Test: Pair of Linear Equations in Two Variables - Question 5

The sum of the numerator and denominator of a fraction is 18. If the denominator is increased by 2, the fraction reduces to 1/3. The fraction is

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 5


RD Sharma Test: Pair of Linear Equations in Two Variables - Question 6

A system of two linear equations in two variables is consistent, if their graphs

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 6

A system of two linear equations in two variables is consistent, if their graphs intersect only at a point, because it has a unique solution.

A system of two linear equations can have one solution, an infinite number of solutions, or no solution. ... If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent .Consistent and Dependent Systems

RD Sharma Test: Pair of Linear Equations in Two Variables - Question 7

The vertices of the triangle formed by the lines x – y + 1 = 0, 3x + 2y – 12 = 0 and the x – axis are

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 7

Here are the two solutions of each of the given equations.x−y+1=03x+2y−12=0


The triangle formed by given two linear equations is shaded in the graph. The triangle formed by given lines is ΔAEF Therefore, the vertices of triangle AEF are A ( –1, 0), E (2, 3) and F (4, 0).

RD Sharma Test: Pair of Linear Equations in Two Variables - Question 8

The pair of equations 5x – 15y = 8 and 3x - 9y = 24/5 has

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 8

Given: a1 = 5,a2 = 3,b1 = −15,b2 = −9,c1 = 8 and 

Therefore, the the pair of given linear equations has infinitely many solutions.

RD Sharma Test: Pair of Linear Equations in Two Variables - Question 9

If x = α and y = β is the solution of the equations x – y = 2 and x + y = 4, then

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 9

Given: x−y = 2…..(i)
And x+y = 4 ………(ii)
Adding eq. (i) and (ii) for elimination of y, we get
2x = 6 ⇒ x = 3
Putting the values of x in eq. (i), we get
3−y = 2 ⇒ y = 1
∴x = α = 3 and y = β = 1

RD Sharma Test: Pair of Linear Equations in Two Variables - Question 10

Half the perimeter of a rectangular garden, whose length is 4m more than its width is 36m. The area of the garden is

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 10

Let the length of rectangular garden be x meters and breadth be y meters. According to question,
x = 4+y ⇒ x−y = 4 ……….(i)
Also half of the perimeter = 36 ⇒ x+y = 36 ……….(ii)
Adding eq. (i) and (ii), we get 2x = 40 ⇒ x = 20 meters
Subtracting eq. (i) from (ii), we get 2y = 32 ⇒ y = 16 meters 
∴ Area = Length x Breadth = 20 x 16 = 320 sq. meters

RD Sharma Test: Pair of Linear Equations in Two Variables - Question 11

A system of two linear equations in two variables is dependentconsistent, if their graphs

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 11

A system of two linear equations in two variables is dependentconsistent, if their graphs coincide with each other.

RD Sharma Test: Pair of Linear Equations in Two Variables - Question 12

One equation of a pair of dependent linear equations is – 5x + 7y = 2, then the second equation can be

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 12

If equation of a pair of dependent linear equations, then 
For satisfying the condition of dependent linear equations, the values of a2,b2 and c2 should be the multiples of the values of a1,b1 and c1
∴ the values would be  and c1 = 2×(−2)=−4
∴ the second equation can be 10x−14y = −4

RD Sharma Test: Pair of Linear Equations in Two Variables - Question 13

The pair of equations x = 2 and y = – 3 has

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 13

Here a unique solution of each variable of a pair of linear equations is given, therefore, it has one solution of a system of linear quations.

RD Sharma Test: Pair of Linear Equations in Two Variables - Question 14

The solution of px + qy = p – q and qx – py = p + q is

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 14





RD Sharma Test: Pair of Linear Equations in Two Variables - Question 15

The difference between two numbers is 26 and one number is three times the other. The numbers are

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 15

Let the two numbers be x and y. 
According to question, x−y = 26 and x = 3y 
Putting the value of x in x−y = 26 we get 3y−y = 26 ⇒ y = 13 And x = 3 × 13 = 39

RD Sharma Test: Pair of Linear Equations in Two Variables - Question 16

The lines representing the pair of equations 5x – 4y + 8 = 0 and 7x + 6y – 9 = 0

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 16

RD Sharma Test: Pair of Linear Equations in Two Variables - Question 17

One equation of a pair of inconsistent linear equations is 2x – 3y = 4, then the second equation can be

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 17

If equation of a pair of inconsistent linear equations, then 
 
For satisfying the condition of dependent linear equations, the values of a2,b2 and c2 should be the multiples of the values of a1,b1 and c1.
∴ the values would be
 ∴ the second equation can be 4x−6y = 8

RD Sharma Test: Pair of Linear Equations in Two Variables - Question 18

The value of ‘k’ so that the system of equations 3x – 4y – 7 = 0 and 6x – ky – 5 = 0 have a unique solution is

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 18


RD Sharma Test: Pair of Linear Equations in Two Variables - Question 19

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 19









RD Sharma Test: Pair of Linear Equations in Two Variables - Question 20

The sum of two numbers is 35 and their difference is 13. The numbers are

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 20

Let the numbers be x and .y. 
According to question, x+y = 35 ………(i) and x−y = 13 ………..(ii)
Adding eq. (i) and (ii), we get  2x = 48 ⇒ x = 24
Putting the value of x in eq. (i), we get 12+y = 35 ⇒ y = 13
Therefore, the numbers are 24 and 13.

RD Sharma Test: Pair of Linear Equations in Two Variables - Question 21

What will be the solution of these equations ax+by = a-b, bx-ay = a+b       

RD Sharma Test: Pair of Linear Equations in Two Variables - Question 22

The area of the triangle formed by x + 3y = 6, 2x – 3y = 12 and the y – axis is

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 22

Here are the two solutions of each of the given equations. x+3y=62x−3y=12


RD Sharma Test: Pair of Linear Equations in Two Variables - Question 23

The value of ‘k’ so that the system of linear equations kx – y – 2 = 0 and 6x – 2y – 3 = 0 have no solution is

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 23


RD Sharma Test: Pair of Linear Equations in Two Variables - Question 24

The pair of linear equations ax + by = c and px + qy = r has a unique solution then

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 24

Given: a1 = a,a2 = p,b1 = b,b2 = q,c1 = c and c2 = r
Since the pair of given linear equations has a unique 

RD Sharma Test: Pair of Linear Equations in Two Variables - Question 25

The value of ‘a’ so that the point (3, a) lies on the line represented by 2x – 3y = 5 is

Detailed Solution for RD Sharma Test: Pair of Linear Equations in Two Variables - Question 25

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