Topic Question Set
Q 11
:
The pair of equations, x = 0 and x = -4 has
a unique solution
no solution
infinitely many solutions
only solution (0, 0)
(2)
Since the lines x = 0 and x = -4 are parallel to each other, therefore there is no solution for the given pair of equations
Q 12
:
If 2x + 3y = 15 and 3x + 2y = 25, then the value of x – y is
–10
8
10
–8
(3)
Given linear equations, we have:
2x + 3y = 15 ...(i)
3x + 2y = 25 ...(ii)
Subtracting (i) from (ii), we get:
x – y = 25 – 15
⇒ x – y = 10
Q 13
:
3 chairs and 1 table cost Rs 900; whereas 5 chairs and 3 tables cost Rs 2,100. If the cost of 1 chair is Rs x and the cost of 1 table is Rs y, then the situation can be represented algebraically as
3x + y = 900, 3x + 5y = 2100
x + 3y = 900, 3x + 5y = 2100
3x + y = 900, 5x + 3y = 2100
x + 3y = 900, 5x + 3y = 2100
(3)
Given situations can be represented algebraically as:
3x + y = 900 and 5x + 3y = 2100
Q 14
:
Tanisha and Aditya have some chocolates with them such that
• If Tanisha were to give 6 chocolates to Aditya, the new quantity of chocolates with each of them would be equal.
• Instead, if Aditya were to give 3 chocolates to Tanisha, then Tanisha would have four times as many chocolates as Aditya initially had.
Which of these pairs of equations would help us find the number of chocolates that they have?
(Note: Assume the initial number of chocolates with Tanisha as 'x' and that with Aditya as 'y'.)
x – 6 = y + 6; x + 3 = 4(y – 3)
x – 6 = y + 6; x + 3 = 4y
x + 6 = y – 6; x – 3 = 4y
x – y = 6; x = y
(2)
Initial number of chocolates with Tanisha = x
Initial number of chocolates with Aditya = y
Case I: x – 6 = y + 6
Case II: x + 3 = 4y
Q 15
:
The sum of the digits of a two-digit number is 9. If 27 is subtracted from the number, its digits are interchanged. Which of these is the product of the digits of the number?
8
14
18
20
(3)
Let x be the unit place digit and y be the ten’s place digit.
Two-digit number = 10y + x
According to the question,
x + y = 9 ...........(i)
10y + x – 27 = 10x + y ⇒ y – x = 3 ...........(ii)
Adding (i) and (ii), we get 2y = 9 + 3 ⇒ y = 6
Putting y = 6 in (i), we get x + 6 = 9 ⇒ x = 3
So, product of the digits of the number = 3 × 6 = 18
