Ncert solutions mathematics class 10 Solutions for Chapter 3 pair of linear equations in two variables

Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” Represent this situation algebraically.

Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” Check whether the following graphical representation of the situation is correct or incorrect.

The coach of a cricket team buys 3 bats and 6 balls for Rs.3900. Later, she buys another bat and 3 more balls of the same kind for Rs.1300. Represent this situation algebraically and select the correct option.

The coach of a cricket team buys 3 bats and 6 balls for Rs.3900. Later, she buys another bat and 3 more balls of the same kind for Rs.1300. Check whether the graph given below is correct according to the given situation.

The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs.160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs.300. Check whether the given graph is correct or incorrect for the given situation.

On comparing the ratio, (a1/a2) , (b1/b2) , (c1/c2) find out whether (3/2)x+(5/3)y = 7; 9x – 10y = 14 are consistent or inconsistent.

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.

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.

On comparing the ratios a₁/a₂ , b₁/b₂ , c₁/c₂ for 5x – 4y + 8 = 0 and 7x + 6y – 9 = 0 it can be concluded that the lines

On comparing the ratios a1/a2 , b1/b2 , c1/c2 for 9x + 3y + 12 = 0 and 18x + 6y + 24 = 0 it can be concluded that the lines

On comparing the ratio, (a1/a2) , (b1/b2) , (c1/c2) find out whether 2x – 3y = 8 ; 4x – 6y = 9 are consistent or inconsistent.

On comparing the ratios a1/a2 , b1/b2 , c1/c2 for 6x – 3y + 10 = 0 and 2x – y + 9 = 0 it can be concluded that the lines

On comparing the ratio, (a₁/a₂) , (b₁/b₂) , (c₁/c₂) find out whether 5x – 3y = 11 ; – 10x + 6y = –22 are consistent or inconsistent.

Find out whether 2x + y – 6 = 0 and 4x – 2y – 4 = 0 are consistent / inconsistent?

Find out whether x + y = 5, 2x + 2y = 10 are consistent / inconsistent?

Find out whether x – y = 8 and 3x – 3y = 16 are consistent / inconsistent?

Given the linear equation 2x + 3y – 8 = 0, which of the following is a linear equation in two variables such that the geometrical representation of the pair so formed is intersecting lines.

Given the linear equation 2x + 3y – 8 = 0, which of the following is a linear equation in two variables such that the geometrical representation of the pair so formed is coincident lines.

Determine the coordinates of the vertices of the triangle formed by the equations x – y + 1 = 0 and 3x + 2y – 12 = 0 and the x-axis.

Given the linear equation 2x + 3y – 8 = 0, which of the following is a linear equation in two variables such that the geometrical representation of the pair so formed is parallel lines.

On comparing the ratio, (a1/a2) , (b1/b2) , (c1/c2) find out whether **3x + 2y = 5 ; 2x – 3y = 7** are consistent or inconsistent.

On comparing the ratio, (a₁/a₂) , (b₁/b₂) , (c₁/c₂) find out whether (4/3)x+2y = 8 ; 2x + 3y = 12 are consistent or inconsistent.

Find out whether 2x – 2y – 2 = 0 and 4x – 4y – 5 = 0 are consistent / inconsistent?

The coach of a cricket team buys 7 bats and 6 balls for Rs.3800. Later, she buys 3 bats and 5 balls for Rs.1750. Find the cost of each bat and each ball.

The difference between two numbers is 26 and one number is three times the other. Find x and y.

Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.

Solve x + y = 14 and x – y = 4 of linear equations by the substitution method and find x and y.

Solve 0.2x + 0.3y = 1.3 and 0.4x + 0.5y = 2.3 of linear equations by the substitution method and find x and y.

The larger of two supplementary angles exceeds the smaller by 18 degrees. Find x and y.

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 Rs 105 and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and the charge per km?

Solve √2 x + √3 y = 0 and √3 x – √8 y = 0 of linear equations by the substitution method and find x and y.

Solve (3x/2)-(5y/3) = -2 and (x/3) + (y/2) = 13/6 of linear equations by the substitution method and find x and y.

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.

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?

Solve 3x – y = 3 and 9x – 3y = 9 of linear equations by the substitution method and find x and y.

Solve: x + y = 5 and 2x – 3y = 4 by the elimination method.

Solve: 3x + 4y = 10 and 2x – 2y = 2 by the elimination method.

Solve 3x – 5y – 4 = 0 and 9x = 2y + 7 by the elimination method and the substitution method.

Solve x/2+ 2y/3 = -1 and x-y/3 = 3 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? Find their solutions (if they exist) by the elimination method.

Meena went to a bank to withdraw Rs.2000. She asked the cashier to give her Rs.50 and Rs.100 notes only. Meena got 25 notes in all. Find how many notes of Rs.50 and Rs.100 she received. Find their solutions (if they exist) 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 Rs.27 for a book kept for seven days, while Susy paid Rs.21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

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.

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? Find their solutions (if they exist) by the elimination method.

For which value of k will the following pair of linear equations have no solution?

3x + y = 1

(2k – 1) x + (k – 1) y = 2k + 1

For which values of a and b does the following pair of linear equations have an infinite number of solutions?

2x + 3y = 7

(a – b) x + (a + b) y = 3a + b – 2

Solve **x – 3y – 3 = 0 and 3x – 9y – 2 = 0** and find whether the linear equation has

Solve **2x + y = 5 and 3x + 2y = 8** and find whether the linear equations has

Which of the following represent the correct nature of the pair of linear equations?

x – 3y – 7 = 0

3x -3y – 15 = 0

Solve **3x – 5y = 20 and 6x – 10y = 40** and find whether the linear equations has

A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs.1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs.1180 as hostel charges. Find the fixed charges and the cost of food per day. Find the solution (if they exist) by any algebraic method.

Solve the following pair of linear equations by the substitution and cross-multiplication methods:

8x + 5y = 9

3x + 2y = 4

A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction. Find the solution (if they exist) by any algebraic method

Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars? Find their solutions (if they exist) by any algebraic method.

Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test? Find their solutions (if they exist) by any algebraic method.

The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle. Find their solutions (if they exist) by any algebraic method.

Solve 2/√x + 3/√y = 2 ; 4/√x + 9/√y = -1 by reducing them to a pair of linear equations.

Solve: \frac{4}{x}+3y=14\ ;\ \frac{3}{x}-4y=23

by reducing them to a pair of linear equations.

Solve 5/(x-1) + 1/(y-2) = 2 ; 6/(x-1) – 3/(y-2) = 1 by reducing them to a pair of linear equations.

Solve 6x + 3y = 6xy ; 2x + 4y = 5xy by reducing them to a pair of linear equations.

Solve 10/(x+y) + 2/(x-y) = 4 ; 15/(x+y) – 5/(x-y) = -2 by reducing them to a pair of linear equations.

2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone. Find the solution.

Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current. Find the solution.

Solve 1/x + 2/y = 2 ; 1/x + 2/y = 1 by reducing them to a pair of linear equations.

Solve **4x + 3y = 6xy ; 4x + 3y = 5xy** by reducing them to a pair of linear equations.

Solve **2/x + 3y = 14 ; 1/x -2y = 3** by reducing them to a pair of linear equations.

Solve 5/x + 1/y= 1 ; 2/x + 5/y = 1 by reducing them to a pair of linear equations.

Roohi travels 300 km to her home partly by train and partly by car. She takes 4 hours if she travels 60 km by train and the remaining by car. If she travels 100 km by train and the remaining by car, she takes 10 minutes longer. Find the speed of the train and the car separately. Find the solution.

Solve the following pair of linear equations:

\frac{7x-2y}{xy}=5\ …\left(1\right)

\frac{8x+7y}{xy}=15\ …\left(2\right)

Solve **2/x + 3/y = 2 ; 4/x – 9/y = -1** by reducing them to a pair of linear equations.

Solve \frac{1}{\ (3x+y)}+\frac{1}{(3x-y)}=\frac{3}{4}\ ;\ \frac{1}{2(3x+y)}-\frac{1}{2(3x-y)}=-\frac{1}{8} by reducing them to a pair of linear equations.

Solve 5/x + 1/y= 2 ; 6/x – 3/y = 1 by reducing them to a pair of linear equations.

Solve 3/x + 1/y = 2 ; 1/x + 3/y = -1 by reducing them to a pair of linear equations.

Solve:

\frac{1}{2x}+\frac{1}{3y}=2\ :\ \frac{1}{3x}+\frac{1}{2y}=\frac{13}{6}

by reducing them to a pair of linear equations.

ABCD is a cyclic quadrilateral. Find the angles of the cyclic quadrilateral.

Solve: 152x − 378y = − 74 ; 76x − 189y = − 37

Solve: x/a – y/b = 0 ; ax + by = a² + b²

Solve: px + qy = p – q ; qx – py = p + q

A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.

The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju.

One says, “Give me a hundred, friend! I shall then become twice as rich as you”. The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their (respective) capital?

The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.

For equations 5x – y = 5 and 3x – y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and the y axis.

In a ∆ABC, ∠C = 3∠B = 2 (∠A + ∠B). Find the three angles.

Solve: (a – b)x + (a + b) y = a² – 2ab – b^{2 ;} (a + b)(x + y) = a² + b²

Solve: ax + by= c ; bx + ay = 1+ c