Pair of Linear Equations in Two Variables MCQs

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A system of equations in two variables having a unique solution, no solutions, or an infinite number of solutions is known as a linear equation in two variables. There may be as many as 'n' variables in a linear system of equations. A straight line is the collection of answers found by solving these linear equations. The algebraic equations of the form y = mx + b, where m is the slope and b is the y-intercept, are known as linear equations in two variables. They're called first-order equations. Two-variable linear equations such as y = 2x+3 and 2y = 4x + 9.

Multiple Choice Questions

Ques. The pairs of equations x+2y-5 = 0 and -4x-8y+20=0 have:
a. Unique solution
b. Exactly two solutions
c. Infinitely many solutions
d. No solution

Ans. Infinitely many solutions

Explanation:

a1/a2 = 1/-4

b1/b2 = 2/-8 = 1/-4

c1/c2 = -5/20 = -¼

This shows:

a1/a2 = b1/b2 = c1/c2

Therefore, the pair of equations has infinitely many solutions.

Ques. The pairs of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 have
a. Unique solution
b. Exactly two solutions
c. Infinitely many solutions
d. No solution

Ans. No solution

Explanation: Given, 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0

a1/a2 = 9/18 = 1/2

b1/b2 = 3/6 = 1/2

c1/c2 = 12/26 = 6/13

Since, a1/a2 = b1/b2 ≠ c1/c2

As a result, the pairs of equations are parallel, and the lines never meet at any point, indicating that there is no solution.

Ques. If the lines 3x+2ky – 2 = 0 and 2x+5y+1 = 0 are parallel, then what is the value of k?
a. 4/15
b. 15/4
c. 4/5
d. 5/4

Ans. 15/4

Explanation: The condition for parallel lines is:

a1/a2 = b1/b2 ≠ c1/c2

Hence, 3/2 = 2k/5

k=15/4

Ques. If one equation of a pair of dependent linear equations is -3x+5y-2=0. The second equation will be:
a. -6x+10y-4=0
b. 6x-10y-4=0
c. 6x+10y-4=0
d. -6x+10y+4=0

Ans. -6x+10y-4=0

Explanation: The condition for dependent linear equations is:

a1/a2 = b1/b2 = c1/c2

For option a,

a1/a2 = b1/b2 = c1/c2= ½

Ques. The solution of the equations x-y=2 and x+y=4 is:
a. 3 and 1
b. 4 and 3
c. 5 and 1
d. -1 and -3

Ans. 3 and 1

Explanation: x-y =2

x=2+y

Substituting the value of x in the second equation we get;

2+y+y=4

2+2y=4

2y = 2

y=1

Now putting the value of y, we get;

x=2+1 = 3

Hence, the solutions are x=3 and y=1.

Ques. A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. The fraction obtained is:
a. 3/12
b. 4/12
c. 5/12
d. 7/12

Ans. 5/12

Explanation: Let the fraction be x/y

So, as per the question given,

(x -1)/y = 1/3 => 3x – y = 3…(1)

x/(y + 8) = 1/4 => 4x –y =8 …..(2)

Subtracting equation (1) from (2), we get

x = 5 ….(3)

Using this value in equation (2), we get,

4×5 – y = 8

y= 12

Therefore, the fraction is 5/12.

Ques. Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Her speed of rowing in still water and the speed of the current is:
a. 6km/hr and 3km/hr
b. 7km/hr and 4km/hr
c. 6km/hr and 4km/hr
strong>d. 10km/hr and 6km/hr

Ans. 6km/hr and 4km/hr

Explanation: Let, Speed of Ritu in still water = x km/hr

Speed of Stream = y km/hr

Now, speed of Ritu, during,

Downstream = x + y km/h

Upstream = x – y km/h

As per the question given,

2(x+y) = 20

Or x + y = 10……………………….(1)

And, 2(x-y) = 4

Or x – y = 2………………………(2)

Adding both the equations, we get,

2x=12

x = 6

Putting the value of x in eq.1, we get,

y = 4

Therefore,

Speed of Ritu is still water = 6 km/hr

Speed of Stream = 4 km/hr

Ques. The angles of cyclic quadrilaterals ABCD are: A = (6x+10), B=(5x)°, C = (x+y)° and D=(3y-10)°. The value of x and y is:
a. x=20° and y = 10°
b. x=20° and y = 30°
c. x=44° and y=15°
d. x=15° and y=15°

Ans. x=20° and y = 30°

Explanation: We know, in cyclic quadrilaterals, the sum of the opposite angles is 180°.

Hence,

A + C = 180°

6x+10+x+y=180 =>7x+y=170°

And B+D=180°

5x+3y-10=180 =>5x+3y=190°

By solving the above two equations we get;

x=20° and y = 30°.

Ques. The pair of equations 5x – 15y = 8 and 3x – 9y = 24/5 has
a. one solution
b. two solutions
c. infinitely many solutions
d. no solution

Ans. infinitely many solutions

Explanation:

The given pair of equations are 5x – 15y = 8 and 3x – 9y = 24/5.

Comparing with the standard form,

a1 = 5, b1 = -15, c1 = -8

a2 = 3, b2 = -9, c2 = -24/5

a1/a2 = 5/3

b1/b2 = -15/-9 = 5/3

c1/c2 = -8/(-24/5) = 5/3

Thus, a1/a2 = b1/b2 = c1/c2

Hence, the given pair of equations has infinitely many solutions.

Ques. The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have
a. a unique solution
b. exactly two solutions
c. infinitely many solutions
d. no solution

Ans. no solution

Explanation:

Given pair of equations are x + 2y + 5 = 0 and –3x – 6y + 1 = 0.

Comparing with the standard form,

a1 = 1, b1 = 2, c1 = 5

a2 = -3, b2 = -6, c2 = 1

a1/a2 = -1/3

b1/b2 = 2/-6 = -1/3

c1/c2 = 5/1

Thus, a1/a2 = b1/b2 ≠ c1/c2

Hence, the given pair of equations has no solution.

Ques. The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is
a. 3
b. -3
c. -12
d. no value

Ans. no value

Explanation:

Given pair of equations are cx – y = 2 and 6x – 2y = 3.

Comparing with the standard form,

a1 = c, b1 = -1, c1 = -2

a2 = 6, b2 = -2, c2 = -3

a1/a2 = c/6

b1/b2 = -1/-2 = 1/2

c1/c2 = -2/-3 = â??

Condition for having infinitely many solutions is

a1/a2 = b1/b2 = c1/c2

c/6 = ½ = â??

Therefore, c = 3 and c = 4

Here, c has different values.

Hence, for no value of c the pair of equations will have infinitely many solutions.

Ques. The graphical representation of a pair of equations 4x + 3y – 1 = 5 and 12x + 9y = 15 will be
a. parallel lines
b. coincident lines
c. intersecting lines
d. perpendicular lines

Ans. parallel lines

Explanation:

Given pair of equations are 4x + 3y – 1 = 5 and 12x + 9y = 15.

Comparing with the standard form,

a1 = 4, b1 = 3, c1 = -6

a2 = 12, b2 = 9, c2 = -15

a1/a2 = 4/12 = 1/3

b1/b2 = 3/9 = 1/3

c1/c2 = -6/-15 = 2/5

Thus, a1/a2 = b1/b2 ≠ c1/c2

Hence, the given pair of equations has no solution.

That means the lines representing the given pair of equations are parallel to each other.

Ques. A pair of linear equations which has a unique solution x = 2, y = -3 is
a. x + y = -1; 2x – 3y = -5
b. 2x + 5y = -11; 4x + 10y = -22
c. 2x – y = 1; 3x + 2y = 0
d. x – 4y – 14 = 0; 5x – y – 13 = 0

Ans. 2x + 5y = -11; 4x + 10y = -22

Explanation:

If x = 2, y = -3 is a unique solution of any pair of equations, then these values must satisfy that pair of equations.

By verifying the options, option (b) satisfies the given values.

LHS = 2x + 5y = 2(2) + 5(- 3) = 4 – 15 = -11 = RHS

LHS = 4x + 10y = 4(2) + 10(- 3)= 8 – 30 = -22 = RHS

Read More-

Pair of Linear Equations In Two Variables Important Questions	Linear Equation in Two Variables: Definition and Graph
Graph of a Linear Equation in Two Variables	Substitution Method of Solving a Pair of Linear Equations
Cross-multiplication method of solving linear equations	Elimination method of solving linear equations
Linear Equation in standard form	Consistent system of linear equations
Differential equation	Inconsistent system

Class	15--20	20--25	25--30	30--35	35--40	40--45
Frequency	12	10	15	11	7	5

Pair of Linear Equations in Two Variables MCQs

Multiple Choice Questions

CBSE X Related Questions

1.
A peacock sitting on the top of a tree of height 10 m observes a snake moving on the ground. If the snake is $10\sqrt{3}$ m away from the base of the tree, then angle of depression of the snake from the eye of the peacock is

2.
In the adjoining figure, $\triangle CAB$ is a right triangle, right angled at A and $AD \perp BC$. Prove that $\triangle ADB \sim \triangle CDA$. Further, if $BC = 10$ cm and $CD = 2$ cm, find the length of AD.

3.
The given figure shows a circle with centre O and radius 4 cm circumscribed by \(\triangle ABC\). BC touches the circle at D such that BD = 6 cm, DC = 10 cm. Find the length of AE.

4.
Find the mean and mode of the following data:
Class 15--20 20--25 25--30 30--35 35--40 40--45
Frequency 12 10 15 11 7 5

5.
Let $p$, $q$ and $r$ be three distinct prime numbers. Check whether $pqr + q$ is a composite number or not. Further, give an example for three distinct primes $p$, $q$, $r$ such that
(i) $pqr + 1$ is a composite number
(ii) $pqr + 1$ is a prime number

6.
The following data shows the number of family members living in different bungalows of a locality:

Number of Members 0−2 2−4 4−6 6−8 8−10 Total
Number of Bungalows 10 p 60 q 5 120

If the median number of members is found to be 5, find the values of p and q.

Similar Mathematics Concepts

Comments

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Pair of Linear Equations in Two Variables MCQs

Multiple Choice Questions

CBSE X Related Questions

1.A peacock sitting on the top of a tree of height 10 m observes a snake moving on the ground. If the snake is $10\sqrt{3}$ m away from the base of the tree, then angle of depression of the snake from the eye of the peacock is

2.In the adjoining figure, $\triangle CAB$ is a right triangle, right angled at A and $AD \perp BC$. Prove that $\triangle ADB \sim \triangle CDA$. Further, if $BC = 10$ cm and $CD = 2$ cm, find the length of AD.

3.The given figure shows a circle with centre O and radius 4 cm circumscribed by \(\triangle ABC\). BC touches the circle at D such that BD = 6 cm, DC = 10 cm. Find the length of AE.

4.Find the mean and mode of the following data:Class15--2020--2525--3030--3535--4040--45Frequency1210151175

5.Let $p$, $q$ and $r$ be three distinct prime numbers. Check whether $pqr + q$ is a composite number or not. Further, give an example for three distinct primes $p$, $q$, $r$ such that (i) $pqr + 1$ is a composite number (ii) $pqr + 1$ is a prime number

6.The following data shows the number of family members living in different bungalows of a locality: Number of Members0−22−44−66−88−10TotalNumber of Bungalows10p60q5120If the median number of members is found to be 5, find the values of p and q.

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
A peacock sitting on the top of a tree of height 10 m observes a snake moving on the ground. If the snake is $10\sqrt{3}$ m away from the base of the tree, then angle of depression of the snake from the eye of the peacock is

2.
In the adjoining figure, $\triangle CAB$ is a right triangle, right angled at A and $AD \perp BC$. Prove that $\triangle ADB \sim \triangle CDA$. Further, if $BC = 10$ cm and $CD = 2$ cm, find the length of AD.

3.
The given figure shows a circle with centre O and radius 4 cm circumscribed by \(\triangle ABC\). BC touches the circle at D such that BD = 6 cm, DC = 10 cm. Find the length of AE.

4.
Find the mean and mode of the following data:
Class 15--20 20--25 25--30 30--35 35--40 40--45
Frequency 12 10 15 11 7 5

5.
Let $p$, $q$ and $r$ be three distinct prime numbers. Check whether $pqr + q$ is a composite number or not. Further, give an example for three distinct primes $p$, $q$, $r$ such that
(i) $pqr + 1$ is a composite number
(ii) $pqr + 1$ is a prime number

6.
The following data shows the number of family members living in different bungalows of a locality:

Number of Members 0−2 2−4 4−6 6−8 8−10 Total
Number of Bungalows 10 p 60 q 5 120

If the median number of members is found to be 5, find the values of p and q.