Linear Equations in Two Variables Test

Question 1
1 / -0

Which of the following equations satisfies the data given in the table below?

x 6 2 -2 0

y 1 -1 -3 -2

A
x = 2y + 4

B
2x = 3 + 9y

C
x + 1 = 2y - 2

D
x = 2y + 2

Question 2
1 / -0

The graph of x = 4 is a line which can said to be

A
parallel to the y - axis at a distance of 4 units from y - axis.

B
parallel to the x - axis at a distance of 4 units from x - axis.

C
making a line which is 4 units long, from the x-axis

D
making a line which is 4 units long, from the y-axis

Question 3
1 / -0

If the line represented by 7y = 2x + c passes through the origin, find the value of x, when y = 12.

A
42

B
24

C
0

D
-14

Question 4
1 / -0

How many linear equations can pass through the point A(3, -12)?

A
Infinitely many

B
Only 144

C
Only 72

D
Only 36

Question 5
1 / -0

The graph of the linear equation 9x + 2y + 18 = 0 is a line which meets the x-axis at the point

A
(-2, 0)

B
(2, 0)

C
(0, 9)

D
(0, -9)

Question 6
1 / -0

In the coordinate system given below, the shaded region is bounded by lines and coordinate axis. Which of the following is not an equation of any of the boundary lines?

A
2x + y = 8

B
x = 0

C
x - 2y = -1

D
x - y = 1

Question 7
1 / -0

Given, (-2k + 1)x + k²y+ c = 0

Find the value of k if the above equation represents linear equation in two variables.

A
0

B

C
Any real value of k, except 0 and

D
None of these

Question 8
1 / -0

For what value of p does the linear equation (p - 1)x + (2p - 5)y = 11 pass through the point (3, 5)?

A
1

B
2

C
3

D
4

Question 9
1 / -0

If C(3, 4) is a point through which the line, x + (2k)y + 13 = 0 passes, then the value of k is

A
-2

B
-1

C
0

D
1

Question 10
1 / -0

Find the area of the triangle formed by the equation, 7x + 5y = 35 and coordinate axes.

A
units

B
units

C
units

D
units

Question 11
1 / -0

A total of 500 tickets to a show are sold. If an adult ticket costs £3, a child ticket costs £2 and a total amount of £1300 is collected, then how many tickets of each kind are sold?

A
Adult tickets = 300
Child tickets = 200

B
Adult tickets = 200
Child tickets = 300

C
Adult tickets = 100
Child tickets = 400

D
Adult tickets = 400
Child tickets = 100

Question 12
1 / -0

Which of the following points satisfies the equation, x - 8y = 12?

A
(4, -1)

B
(-2, 3)

C
(2, 3)

D
(3, 2)

Question 13
1 / -0

For what value of x and y will the value of k be 4 in the given equation?

A
(11, -2)

B
(11, 2)

C
(-11, -2)

D
(-11, 2)

Question 14
1 / -0

If 7x + 4y = 18 and x - y = 0, then find the value of 11(x + y).

A

B

C
12

D
36

Question 15
1 / -0

How many non-negative integer pairs (x, y) satisfy the equation 3x + 4y = 21?

A
0

B
1

C
2

D
3

Question 16
1 / -0

Which of the following is the graphical representation of 2y + 3x = 12?

A

B

C

D

Question 17
1 / -0

The population of city A is x and that of city B is y. If population of city A is 7,00,000 less than three times the population of city B, then:

(1)What will be the linear equation for the given data?
(2) If the population of City A is 8,00,000 then what is the difference between the population of city A and city B?

A
3y = x + 7,00,000; 3,00,000

B
3y = x + 7,00,000; 2,00,000

C
3y = x - 7,00,000; 3,00,000

D
3x = y + 7,00,000; 3,00,000

Question 18
1 / -0

The cost of getting a house painted is Rs. 500 less than half the cost of getting it plastered. If the cost of plastering the house is Rs. x and the cost of painting the house is Rs. y, then write a linear equation to represent this situation.

A
2y + 1000 = x

B
y + 500 = x

C
2y + x = 1000

D
y + x = 1000

Question 19
1 / -0

Aman and Ankit's present ages are 'x' years and 'y' years, respectively. If Aman's age will be 5 year more than half of Ankit's age 3 years from now, then find the linear equation that represents the correct relation regarding the present age of Aman and Ankit.

A
2x - 7 = y

B
2x + y = 7

C
2x - 6 = y

D
2x - 5 = y

Question 20
1 / -0

The price of an eraser Rs. x is Rs. 2.5 less than the price of three sharpeners. If the price of 5 sharpeners is Rs. 2y, then find the equation that represents the price of one eraser.

A
5x + 12.5 = 6y

B
5x + 11.5 = 6y

C
5x + 12.5 = 5y

D
5x + 11.5 = 5y

Question 21
1 / -0

Which of the following statements is true according to the given graph?

A
The linear equations, y – 24 + 3x = 0 and 2x – y = 2, represent the given graph.

B
The linear equations, 14y – 56 + 7x = 0 and 2x – 2y = -2, represent the given graph.

C
The linear equations, 6y – 12 + 37x = 0 and x – 7y = 2, represent the given graph.

D
The linear equations, y – 13 + 4x = 0 and x – 2y = 3, represent the given graph.

Question 22
1 / -0

A car starts moving with a speed of 1.56 ms^-1. It is changes its speed with time, and the time is represented by y seconds. The new speed of the car is represented by x ms^-1. The relation between the final speed and the initial speed is given below:
x = 1.56 + (y)

(1) What will be the speed of the car after 1.5 minutes?
(2) At what time will the final speed of the car be 9.36 ms^-1?

A

(1) (2)

55.56 ms^-1 13 seconds

B

(1) (2)

57.44 ms^-1 24 seconds

C

(1) (2)

60.45 ms^-1 31 seconds

D

(1) (2)

61.56 ms^-1 32 seconds

Question 23
1 / -0

Fill in the blanks.

(I) In the linear equation, 2ax – 10by + 2c = 0 if x = -2, then the value of y is _____A______.
(II) For the linear equation 2x – 8y = 0, _____B_____ point does not lie on the graph.
(III) If the point (1, -1) lies on the graph of the equation, 3ax + 6y – 3 = 0, then the value of 2a is ______C_____.
(IV) By comparing the linear equation,y +x + 1 = 0 with= 1, the value of is _____D____.

A

(A) (B) (C) (D)

(1, 1) (6)

B

(A) (B) (C) (D)

(4, 1) (3)

C

(A) (B) (C) (D)

(8, 2) (2)

D

(A) (B) (C) (D)

(12, 3) (6)

Question 24
1 / -0

Which of the following is the graph of 4y + 5x = 1 and 2x - 3y = 5?

A

B

C

D

Question 25

1 / -0

Match the columns.

Column - I	Column - II
(P) A has 15 pens more than twice the number of pens with B. If 'x' represents the number of pens of A and 'y' represents the number of pens of B, then which equation will represent this situation?	(i) (2x - y) = 15
(Q) Pia scored 15 less than twice the marks scored by Ria in a Science test. If 'x' represents the marks of Ria and 'y' represents the marks of Pia, then which equation will represent this situation?	(ii) (x - 2y) = 15
(R) Aman's present age is 15 years more than Rajesh's age. If Aman's age is represented by 'x' and Rajesh's age is represented by 'y', then which equation will represent this situation?	(iii) (2x - 15y) = 0
(S) Twice the cost of a bat is 15 times the the cost of a ball. If the cost of the bat is 'x' and the cost of the ball is 'y', then which equation will represent this situation?	(iv) (x - y) = 15

(1)	(2)
55.56 ms^-1	13 seconds

(1)	(2)
57.44 ms^-1	24 seconds

(1)	(2)
60.45 ms^-1	31 seconds

(1)	(2)
61.56 ms^-1	32 seconds

Linear Equation...

Question 1

x = 2y + 4

2x = 3 + 9y

x + 1 = 2y - 2

x = 2y + 2

Question 2

parallel to the y - axis at a distance of 4 units from y - axis.

parallel to the x - axis at a distance of 4 units from x - axis.

making a line which is 4 units long, from the x-axis

making a line which is 4 units long, from the y-axis

Question 3

42

24

0

-14

Question 4

Infinitely many

Only 144

Only 72

Only 36

Question 5

(-2, 0)

(2, 0)

(0, 9)

(0, -9)

Question 6

2x + y = 8

x = 0

x - 2y = -1

x - y = 1

Question 7

0

Any real value of k, except 0 and

None of these

Question 8

1

2

3

4

Question 9

-2

-1

0

1

Question 10

units

units

units

units

Question 11

Adult tickets = 300Child tickets = 200

Adult tickets = 200Child tickets = 300

Adult tickets = 100Child tickets = 400

Adult tickets = 400Child tickets = 100

Question 12

(4, -1)

(-2, 3)

(2, 3)

(3, 2)

Question 13

(11, -2)

(11, 2)

(-11, -2)

(-11, 2)

Question 14

12

36

Question 15

0

1

2

3

Question 16

Question 17

3y = x + 7,00,000; 3,00,000

3y = x + 7,00,000; 2,00,000

3y = x - 7,00,000; 3,00,000

3x = y + 7,00,000; 3,00,000

Question 18

Adult tickets = 300
Child tickets = 200

Adult tickets = 200
Child tickets = 300

Adult tickets = 100
Child tickets = 400

Adult tickets = 400
Child tickets = 100

(1) (2)

55.56 ms^-1 13 seconds

(1) (2)

57.44 ms^-1 24 seconds

(1) (2)

60.45 ms^-1 31 seconds

(1) (2)

61.56 ms^-1 32 seconds

(A) (B) (C) (D)

(1, 1) (6)

(A) (B) (C) (D)

(4, 1) (3)

(A) (B) (C) (D)

(8, 2) (2)

(A) (B) (C) (D)

(12, 3) (6)

(P) (Q) (R) (S)

(ii) (iv) (i) (iii)

(P) (Q) (R) (S)

(iii) (i) (iv) (ii)

(P) (Q) (R) (S)

(ii) (i) (iv) (iii)

(P) (Q) (R) (S)

(iv) (iii) (ii) (i)