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03
NCERT Solutions · Maths Ch 3
Pair of Linear Equations in Two Variables
41 questions · 3 exercises
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Ex 3.1
Ex 3.2
Ex 3.3
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
19 QUESTIONS
Exercise 3.1
Q1(i)
Form the pair of linear equations in the following problem, and find its solution graphically: 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.
(3 marks)
Q1(ii)
Form the pair of linear equations in the following problem, and find its solution graphically: 5 pencils and 7 pens together cost ₹50, whereas 7 pencils and 5 pens together cost ₹46. Find the cost of one pencil and that of one pen.
(3 marks)
Q2(i)
On comparing the ratios a₁/a₂, b₁/b₂ and c₁/c₂, find out whether the lines representing the following pair of linear equations intersect at a point, are parallel or coincident: 5x – 4y + 8 = 0 ; 7x + 6y – 9 = 0
(2 marks)
Q2(ii)
On comparing the ratios a₁/a₂, b₁/b₂ and c₁/c₂, find out whether the lines representing the following pair of linear equations intersect at a point, are parallel or coincident: 9x + 3y + 12 = 0 ; 18x + 6y + 24 = 0
(2 marks)
Q2(iii)
On comparing the ratios a₁/a₂, b₁/b₂ and c₁/c₂, find out whether the lines representing the following pair of linear equations intersect at a point, are parallel or coincident: 6x – 3y + 10 = 0 ; 2x – y + 9 = 0
(2 marks)
Q3(i)
On comparing the ratios a₁/a₂, b₁/b₂ and c₁/c₂, find out whether the following pair of linear equations is consistent or inconsistent: 3x + 2y = 5 ; 2x – 3y = 7
(2 marks)
Q3(ii)
On comparing the ratios a₁/a₂, b₁/b₂ and c₁/c₂, find out whether the following pair of linear equations is consistent or inconsistent: 2x – 3y = 8 ; 4x – 6y = 9
(2 marks)
Q3(iii)
On comparing the ratios a₁/a₂, b₁/b₂ and c₁/c₂, find out whether the following pair of linear equations is consistent or inconsistent: (3/2)x + (5/3)y = 7 ; 9x – 10y = 14
(2 marks)
Q3(iv)
On comparing the ratios a₁/a₂, b₁/b₂ and c₁/c₂, find out whether the following pair of linear equations is consistent or inconsistent: 5x – 3y = 11 ; –10x + 6y = –22
(2 marks)
Q3(v)
On comparing the ratios a₁/a₂, b₁/b₂ and c₁/c₂, find out whether the following pair of linear equations is consistent or inconsistent: (4/3)x + 2y = 8 ; 2x + 3y = 12
(2 marks)
Q4(i)
Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically: x + y = 5, 2x + 2y = 10
(3 marks)
Q4(ii)
Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically: x – y = 8, 3x – 3y = 16
(2 marks)
Q4(iii)
Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically: 2x + y – 6 = 0, 4x – 2y – 4 = 0
(3 marks)
Q4(iv)
Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically: 2x – 2y – 2 = 0, 4x – 4y – 5 = 0
(2 marks)
Q5
Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.
(3 marks)
Q6(i)
Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is: intersecting lines
(1 mark)
Q6(ii)
Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is: parallel lines
(1 mark)
Q6(iii)
Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is: coincident lines
(1 mark)
Q7
Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.
(3 marks)
2
13 QUESTIONS
Exercise 3.2
Q1(i)
Solve the following pair of linear equations by the substitution method: x + y = 14 ; x – y = 4
(2 marks)
Q1(ii)
Solve the following pair of linear equations by the substitution method: s – t = 3 ; s/3 + t/2 = 6
(2 marks)
Q1(iii)
Solve the following pair of linear equations by the substitution method: 3x – y = 3 ; 9x – 3y = 9
(2 marks)
Q1(iv)
Solve the following pair of linear equations by the substitution method: 0.2x + 0.3y = 1.3 ; 0.4x + 0.5y = 2.3
(2 marks)
Q1(v)
Solve the following pair of linear equations by the substitution method: √2x + √3y = 0 ; √3x – √8y = 0
(2 marks)
Q1(vi)
Solve the following pair of linear equations by the substitution method: 3x/2 – 5y/3 = –2 ; x/3 + y/2 = 13/6
(2 marks)
Q2
Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.
(3 marks)
Q3(i)
Form the pair of linear equations for the following problem and find its solution by substitution method: The difference between two numbers is 26 and one number is three times the other. Find them.
(3 marks)
Q3(ii)
Form the pair of linear equations for the following problem and find its solution by substitution method: The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
(3 marks)
Q3(iii)
Form the pair of linear equations for the following problem and find its solution by substitution method: The coach of a cricket team buys 7 bats and 6 balls for ₹3800. Later, she buys 3 bats and 5 balls for ₹1750. Find the cost of each bat and each ball.
(3 marks)
Q3(iv)
Form the pair of linear equations for the following problem and find its solution by substitution method: The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is ₹105 and for a journey of 15 km, the charge paid is ₹155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?
(3 marks)
Q3(v)
Form the pair of linear equations for the following problem and find its solution by substitution method: A fraction becomes 9/11, if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes 5/6. Find the fraction.
(3 marks)
Q3(vi)
Form the pair of linear equations for the following problem and find its solution by substitution method: Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?
(3 marks)
3
9 QUESTIONS
Exercise 3.3
Q1(i)
Solve the following pair of linear equations by the elimination method and the substitution method: x + y = 5 and 2x – 3y = 4
(3 marks)
Q1(ii)
Solve the following pair of linear equations by the elimination method and the substitution method: 3x + 4y = 10 and 2x – 2y = 2
(3 marks)
Q1(iii)
Solve the following pair of linear equations by the elimination method and the substitution method: 3x – 5y – 4 = 0 and 9x = 2y + 7
(3 marks)
Q1(iv)
Solve the following pair of linear equations by the elimination method and the substitution method: x/2 + 2y/3 = –1 and x – y/3 = 3
(3 marks)
Q2(i)
Form the pair of linear equations in the following problem, and find its solution (if it exists) by the elimination method: If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 1/2 if we only add 1 to the denominator. What is the fraction?
(3 marks)
Q2(ii)
Form the pair of linear equations in the following problem, and find its solution (if it exists) by the elimination method: Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
(3 marks)
Q2(iii)
Form the pair of linear equations in the following problem, and find its solution (if it exists) by the elimination method: The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
(3 marks)
Q2(iv)
Form the pair of linear equations in the following problem, and find its solution (if it exists) by the elimination method: Meena went to a bank to withdraw ₹2000. She asked the cashier to give her ₹50 and ₹100 notes only. Meena got 25 notes in all. Find how many notes of ₹50 and ₹100 she received.
(3 marks)
Q2(v)
Form the pair of linear equations in the following problem, and find its solution (if it exists) by the elimination method: A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹27 for a book kept for seven days, while Susy paid ₹21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
(3 marks)