Short Answer Questions: Pair of Linear Equations in Two Variables

# 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:

Ans:

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:

Ans:

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

Q13: Solve for x and y:

x + y ≠ 0
x – y ≠ 0
Ans:

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

Ans:

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).

The document Class 10 Maths Chapter 3 Question Answers - Pair of Linear Equations in Two Variables is a part of the Class 10 Course Mathematics (Maths) Class 10.
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## Mathematics (Maths) Class 10

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

 1. What is a pair of linear equations in two variables?
Ans. A pair of linear equations in two variables is a set of two equations that involve two variables and can be represented graphically as two lines on a coordinate plane.
 2. How can a pair of linear equations in two variables be solved?
Ans. A pair of linear equations in two variables can be solved using various methods such as substitution, elimination, and graphing.
 3. What is the significance of finding the solution to a pair of linear equations in two variables?
Ans. Finding the solution to a pair of linear equations in two variables helps in determining the point of intersection of the two lines represented by the equations on a coordinate plane.
 4. Can a pair of linear equations in two variables have no solution?
Ans. Yes, a pair of linear equations in two variables can have no solution if the lines represented by the equations are parallel and do not intersect at any point.
 5. How can the consistency of a pair of linear equations in two variables be determined?
Ans. The consistency of a pair of linear equations in two variables can be determined by analyzing the slopes of the lines represented by the equations. If the slopes are equal, the equations are consistent and have infinitely many solutions.

## Mathematics (Maths) Class 10

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