Linear Equations in Two Variables Test

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Linear Equations in Two Variables Test - 7

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Weekly Quiz Competition

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

Solution

x = 2y + 4 satisfies all of the given sets of data, i.e.

(1) x = 2y + 4
6 = 2(1) + 4
6 = 6

(2) x = 2y + 4
2 = 2(-1) + 4
2 = 4 - 2
2 = 2

(3) x = 2y + 4
-2 = 2(-3) + 4
-2 = -6 + 4
-2 = -2

(4) x = 2y + 4
0 = 2(-2) + 4
0 = 0

Hence, option 1 is the correct answer.
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

Solution

The graph of x = 4 is a line which can said to be parallel to the y-axis at a distance of 4 units from 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

Solution

7y = 2x + c, passes through origin, i.e.
x = 0, y = 0, or (0, 0)
Putting the value of x = 0 and y = 0 in the equation we get,
7(0) = 2(0) + c
c = 0

Therefore, c must be 0, i.e.
7y = 2x

If y = 12, then x will be 7(12) = 2(x)
84 = 2(x)

x =
x = 42
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

Solution

Since any number of linear equations can be made to pass through the point A(3, -12), the answer to this question will be option 1.
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)

Solution

9x + 2y + 18 = 0
9x + 2y = -18
Since this line meets the x-axis, the value of y is 0, i.e. y = 0

9x + 2(0) = -18
9x = -18
x =
x = -2
Thus, the coordinates of the point will be (-2, 0).
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

Solution

Shaded part is enclosed by 3 lines.
The equation of the line on y-axis: x = 0
The equation of the line passing through points (0, 8) and (3, 2): 2x + y = 8
Testing point (0, 8) in equation, 2x + y = 8
2(0) + 8 = 8
8 = 8
Testing point (3, 2) in equation, 2x + y = 8
2(3) + 2 = 8
6 + 2 = 8
8 = 8
The equation of the line passing through points (3, 2) and (0, -1): x - y = 1
Testing point (3, 2) in equation, x - y = 1
3 - 2 = 1
Testing point (0, -1) in equation, x - y = 1
0 - (-1) = 1
1 = 1
Only the equation, x - 2y = -1 is not used in the given graph.
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

Solution

For linear equation in two variables, the coefficients of x and y should not be equal to 0.
So,
-2k + 1 ≠ 0
-2k ≠ -1

k ≠

Also,
k²≠ 0
k ≠ 0

Hence, option 3 is the correct answer.
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

Solution

x = 3 and y = 5
(p - 1)3 + (2p - 5)5 = 11
3p - 3 + 10p - 25 = 11
3p + 10p = 11 + 25 + 3
13p = 39
p = 3
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

Solution

x + (2k)y + 13 = 0 and C(3, 4)
Using x = 3 and y = 4,
3 + (2k)4 + 13 = 0
3 + 8k + 13 = 0
8k = -16
k = -2
The value of k will be -2.
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

Solution

The given equation is 7x + 5y = 35.
(1) When it passes through x-axis, y co-ordinate will be 0.
i.e. y = 0
7x + 5(0) = 35
7x + 0 = 35
7x = 35
x = 5
(2) When it passes through y-axis, x co-ordinate will be 0.
i.e. x = 0
7(0) + 5(y) = 35
5y = 35
y = 7
The two co-ordinates will be
(0, 7) and (5, 0)

Area of the triangle = × b × h
= × 5 × 7

= 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

Solution

Let the number of adult tickets sold be x and the number of child tickets sold be y.
Total number of tickets sold = 500
x + y = 500
y = 500 - x
According to the question:
3x + 2y = 1300
3x + 2(500 - x) = 1300
3x + 1000 - 2x = 1300
x + 1000 = 1300
x = 1300 - 1000 = 300
So, number of adult tickets sold = 300
Number of child tickets sold = y = 500 - x
= 500 - 300
= 200
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)

Solution

x - 8y = 12
Let x = 4 and y = -1
4 - (8 (-1)) = 12
4 + 8 = 12
12 = 12
Therefore, the co-ordinates of this point satisfy the equation.
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)

Solution

Given equation:

Going by option 1:
Putting x = 11 and y = -2,
= k
= k
2 - (-2) = k
2 + 2 = k
k = 4
This satisfies the value of k.

Going by option 2:
Putting x = 11 and y = 2,
2 - 2 = k
k = 0
This does not satisfy the value of k.

Going by option 3:
Putting x = -11 and y = -2,

-8/3 + 2 = k
k = -2/3
This does not satisfy the value of k.

Going by option 4:
Putting x = -11 and y = 2,
-8/3 - 2 = k
k = -14/3
This does not satisfy the value of k.
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

Solution

7x + 4y = 18 … (1)
Now, x - y = 0
Or x = y
Put x = y in equation (1).
7y + 4y = 18
11y = 18
Now, x = y
11x = 11y = 18
Now, 11(x + y) = 11x + 11y
= 18 + 18
= 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

Solution

x and y are non-negative integers. (Given)
Start from x = 0.
If x = 0, 1, or 2, y cannot be an integer.
For x = 3, y = 3
And for x = 7, y = 0
These two pairs only satisfy the given equation.
Question 16
1 / -0

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

A

B

C

D

Solution

2y + 3x = 12
When x = 0, then y = 6
When y = 0, then x = 4
Option (2) is correct.
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

Solution

Given that population of city A be x and that of city B be y.

(1)
A.T.Q, 3y - 7,00,000 = x
3y = x + 7,00,000
(2)
If population of city A is x = 8,00,000

A.T.Q,

3y - 7,00,000 = x
3y - 7,00,000 = 8,00,000
3y = 7,00,000 + 8,00,000
3y = 15,00,000
y = 15,00,000 ÷ 3
y = 5,00,000

Therefore, population of city B: (y) = 5,00,000

Difference between the population of city A and city B = 8,00,000 - 5,00,000 = 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

Solution

Given:
Cost of painting the house is Rs. y and Cost of plastering the house is Rs. x.

y =

y + 500 =

2y + 1000 = x
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

Solution

Aman's age = x years
Ankit's age = y years
According to the question,

x + 3 =

x + 3 =
2x + 6 = y + 13
2x + 6 - 13 = y
2x - 7 = 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

Solution

Price of one eraser = Rs. x
Price of five sharpeners = 2y

Price of one sharpener =

Price of three sharpeners = =
We know that the price of an eraser is Rs. 2.5 less than the price of three sharpeners.
Therefore,

x =
x + 2.5 =

5x + 12.5 = 6y
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.

Solution

y = mx+b

Where,

m is the slope, and b is the y-intercept

m =

Given points are (2, 3) and (-2, 5)

m = = =

y = .................(1)

Put (2, 3) in (1)

3 =

3 + 1 = b

b = 4

So

y =

y + - 4 = 0

Multiply both sides by 14

14y + 7x - 56 = 0

For the second equation given points are (1,2) and (4,5)

m =

y = x + b ......... (2)

Put the points (1,2) in (2)

2 = 1 + b

b = 1

y = x + 1

-1 = x - y or x - y = -1

Multiply both sides by 2

2x - 2y = -2

Hence, option 2 is correct.
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

Solution

(1) x = 1.56 + (y)
Here, x = speed of the car in ms^-1
y = time in seconds

1 minute = 60 seconds
y = 1.5 × 60 = 90 seconds
So,
x = 1.56 + × 90

x = 1.56 + 54
x = 55.56 ms^-1

(2) x = 1.56 + (y)
Here,
x = speed of the car in ms^-1
y = time in seconds

9.36 = 1.56 + (y)

9.36 – 1.56 = (y)
7.8 × 5 = 3y

13 seconds = y
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)

Solution

(I) 2ax – 10by + 2c = 0
If x = -2, then the equation will become:
2a(-2) – 10by + 2c = 0
-4a – 10by = -2c
-10by = -2c + 4a

y =
y =

(II) 2x – 8y = 0
Point (1, 1)
2(1) – 8(1) = 0
2 – 8 = 0
-6 = 0 --- This is not true.
So, this point does not lie on the graph of this linear equation.

(III) 3ax + 6y – 3 = 0
Point (1, -1)
So,
x = 1, y = -1
3a(1) + 6(-1) – 3 = 0
3a - 6 – 3 = 0
3a = 9
a = 3
So,
2a = 2 × 3 = 6

(IV) y +x + 1 = 0
= 0
14y + 3x + 21 = 0
3x + 14y = -21
Or 3x - (-14)y = -21 ... (1)

Standard form,
= 1
ax – by = c

Comparing with eq (1),

a = 3, b = -14
So,
=
Question 24
1 / -0

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

A

B

C

D

Solution

The lines can be plotted as:

5x + 4y = 1

x 1 -3

y -1 4

2x - 3y = 5

x 1 -2 4

y -1 -3 1

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

(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)

Solution

(P) Number of pens of A = x
Number of pens of B = y
According to the question,
x = 15 + 2y
This means,
(x – 2y) = 15

(Q) Pia's marks = y
Ria's marks = x
According to the question,
y = 2x - 15
(2x - y) = 15

(R) Aman's age = x
Rajesh's age = y
According to the question,
x = y + 15
(x – y) = 15

(S) Cost of bat = x
Cost of ball = y
According to the question,
2x = 15y
(2x – 15y) = 0

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(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 Equations in Two Variables Test - 7

Result

Linear Equations in Two Variables Test - 7

Score

-

Rank

-

SHARING IS CARING

Question 1

x = 2y + 4

2x = 3 + 9y

x + 1 = 2y - 2

x = 2y + 2

Solution

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

Solution

Question 3

42

24

0

-14

Solution

Question 4

Infinitely many

Only 144

Only 72

Only 36

Solution

Question 5

(-2, 0)

(2, 0)

(0, 9)

(0, -9)

Solution

Question 6

2x + y = 8

x = 0

x - 2y = -1

x - y = 1

Solution

Question 7

0

Any real value of k, except 0 and

None of these

Solution

Question 8

1

2

3

4

Solution

Question 9

-2

-1

0

1

Solution

Question 10

units

units

units

units

Solution

Question 11

Adult tickets = 300Child tickets = 200

Adult tickets = 200Child tickets = 300

Adult tickets = 100Child tickets = 400

Adult tickets = 400Child tickets = 100

Solution

Question 12

(4, -1)

(-2, 3)

(2, 3)

(3, 2)

Solution

Question 13

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)