Class 10 Maths Chapter 3 Question Answers - Pair of Linear Equations in Two Variables

Q1: The sum of the digits of a two digit number is 8 and the difference between the number and that formed by reversing the digits is 18. Find the number.
Ans: Let unit and tens digit be x and y.
∴ Original number = 1x + 10y …(i)
Reversed number = 10x + 1y
According to question,
x + y = 8
⇒ y = 8 – x …(ii)
Also, 1x + 100y – (10x + y) = 18
⇒ x + 10y – 10x – y = 18
⇒ 9y – 9x = 18
⇒ y – x = 2 …[Dividing both sides by 9
⇒ 8 – x – x = 2 …[From (it)
⇒ 8 – 2 = 2x
⇒ 2x = 6
From (it), y = 8 – 3 = 5
From (i), Original number = 3 + 10(5) = 53

Q2: A man earns ₹600 per month more than his wife. One-tenth of the man’s salary and l/6th of the wife’s salary amount to ₹1,500, which is saved every month. Find their incomes.
Ans: Let wife’s monthly income = ₹x
Then man’s monthly income = ₹(x + 600)
According to the question,

Wife’s income = ₹x = ₹5,400
Man’s income = ₹(x + 600) = ₹6,000

Q3: Solve the following pair of linear equations by the cross multiplication method: x + 2y = 2; x – 3y = 7
Ans: x + 2y – 2 = 0
x – 3y – 7 = 0


Q4: Find the value of a and p for which the following pair of linear equations has infinite number of solutions:
2x + 3y = 7;
αx + (α + β)y = 28 (2013)
Ans: We have, 2x + 3y = 7 and αx + (α + β)y = 28


Q5: Find the two numbers whose sum is 75 and difference is 15.
Ans: Let the two numbers be x and y.
According to the question,
x + y = 75 …(i)
∴ x – y = ±15 …(ii)
Solving (i) and (ii), we get

Q6: Solve the following pair of equations:
49x + 51y = 499
51x + 49 y = 501
Ans:


Q7: Solve:

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Q8: Solve for x and y:
27x + 31y = 85;
31x + 2 7y = 89
Ans:

Putting the value of ‘x’ in (i), we get
2 + y = 3 ⇒ y = 3 – 2 = 1
∴ x = 2, y = 1

Q9: Solve by elimination:
3x – y – 7
2x + 5y + 1 = 0
Ans: 3 x – y = 7 …(i)
2x + 5y = -1 -00
Multiplying equation (i) by 5 & (ii) by 1,

⇒ x = 2
Putting the value of x in (i), we have
3(2) - y = 7 ⇒ 6 – 7 = y
∴ y = -1 ∴ x = 2, y = -1

Q10: Solve by elimination:
3x = y + 5
5x – y = 11
Ans: We have, 3x = y + 5, and 5x – y = 11

Putting the value of x in (i), we get
3x – y = 5 ⇒ 3(3) – y = 5
9 – 5 = y ⇒ y = 4
∴ x = 3, y = 4

Q11: Solve the following pair of linear equations for x and y:

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Q12: Solve the following pair of linear equations for x and y:
141x + 93y = 189;
93x + 141y = 45
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Q13: Solve for x and y:

x + y ≠ 0
x – y ≠ 0
Ans: 



Q14: Solve the following pair of equations for x and y:

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Q15: Represent the following pair of equations graphically and write the coordinates of points where the lines intersect y-axis.
Ans:

By plotting the points and joining them, the lines intersect at A (6, 0).
Line x + 3y = 6 intersects y-axis at B(0, 2) and Line 2x – 3y = 12 intersects y-axis at C(0, -4).