Linear Equations in Two Variables Test

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Linear Equations in Two Variables Test - 13

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Weekly Quiz Competition

Question 1
1 / -0

If the line ax + by + c = 0 is parallel to x-axis, then which of the following relations is correct?

A
a = 0

B
b = 0

C
c = 0

D
a = b

Solution

The equation of a line parallel to the x-axis is of the form y = k, where k is a constant.

Therefore, the coefficient of x should be zero.

∴ a = 0

Thus, the relation given in alternative A is correct.

Hence, the correct answer is option A.
Question 2
1 / -0

Use the following information to answer the next question.

The weight of 5 hens and 6 pigeons is 19.5 kg whereas the weight of 1 hen and 3 pigeons is 7.5 kg.

Assuming that all the hens are of same weight and all the pigeons are of same weight, then what is the weight of 8 hens and 6 pigeons?

A
23.5 kg

B
24 kg

C
25.5 kg

D
26 kg

Solution

Let the weight of 1 hen and 1 pigeon be h and p respectively.

According to given information:

5h + 6p = 19.5 … (1)

h + 3p = 7.5 … (2)

Subtracting equation (2) from (1):

(5h + 6p) − (h + 3p) = 19.5 − 7.5

⇒ 4h + 3p = 12

⇒ 2 (4h + 3p) = 2 × 12

⇒ 8h + 6p = 24

Thus, the weight of 8 hens and 6 pigeons is 24 kg.

The correct answer is B.

Question 3

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Use the following information to answer the next question.

Ashu hired a cab in the night to go to a party. The cab provider told him that he will charge Rs 1000 for the cab and an extra charge of Rs 100 will be applicable for each hour after 12:00 a.m.

Ashu used the cab for x hours more after 12:00 a.m. If y is the total amount paid by Ashu, then which equation represents the given situation?

y + 100x = 1000

y + 1000 = 100x

y = 1000 + 100x

y + 100x + 1000 = 0

Solution

It is given that y is the amount paid by Ashu.

It is also given that Ashu used the cab for x hours more after 12:00 a.m.

Therefore, the charge for those x hours is Rs 100x.

Thus, the equation representing the given situation is: y = 1000 + 100x

The correct answer is C.

Question 4
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Use the following information to answer the next question.

The ages of Bob and his father are related by the expression y = 4x − 5 where x is Bob’s age and y is his father’s age.

Which of the following conclusions is true about the given expression?

A
Bob’s father’s age is five less than four times Bob’s age

B
Bob’s father’s age is four less than five times Bob’s age

C
Bob’s father’s age is four times Bob’s age

D
Bob’s father’s age as five times Bob’s age

Solution

The expression is y = 4x − 5

x = Bob’s age

y = Bob’s father age

Therefore, it can be seen that Bob’s father’s age is five less than four times Bob’s age.

The correct answer is A.
Question 5
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Use the following information to answer the next question.

x

3

5

7

9

11

13

y

5

7

9

11

13

15

Which of the following equations satisfies the values of x and y in the given table?

A
y = x − 2

B
x = y − 3

C
x = y + 3

D
y = x + 2

Solution

If x = 3, y = 3 + 2 = 5

If x = 5, y = 5 + 2 = 7

If x = 7, y = 7 + 2 = 9

If x = 9, y = 9 + 2 = 11

If x = 11, y = 11 + 2 = 13

If x = 13, y = 13 + 2 = 15

Thus, the rule followed in the given table is y = x + 2

The correct answer is D.