Linear Equations in Two Variables | Class 10 | Problem Set 1

Linear Equations in Two Variables | Class 10 | Problem Set 1

Linear Equations in Two Variables | Class 10 | Problem Set 1 | Simple solutions of all the examples are available in this article.

The pdf file attached at the end of this article contains simple solutions of all the examples of problem set 1.

Also read : Linear Equations in Two Variables | Class 10 | Practice Set 1.1

Also read : Linear Equations in Two Variables | Class 10 | Practice Set 1.2

In this article, you will get the simple solutions of all the examples, given in the problem set 1 of linear equations in two variables.

In this problem set, all the examples are solved using the methods provided in the chapter. The methods used in this problem set are elimination method, graphical method, Cramer rule and special method of solving linear equations. All the word problems given in this problem set are also solved using the appropriate methods.

Also read : Linear Equations in Two Variables | Class 10 | Practice Set 1.3

Also read : Linear Equations in Two Variables | Class 10 | Practice Set 1.4

Also read : Linear Equations in Two Variables | Class 10 | Practice Set 1.5

Problem Set – 1

1. Choose correct alternative for each of the following questions (1) To draw graph of 4x + 5y = 19, Find y when x = 1.
   (A) 4 (B) 3 (C) 2 (D) -3
   (2) For simultaneous equations in variables x and y, Dx = 49, Dy = -63,
   D = 7 then what is x ? (A) 7 (B) -7
   1 (C) 7
   −1 (D) 7
   (3) Find the value of
   53 -7 -4
   (A) -1 (B) -41
   (4) To solve x + y = 3 ; 3x – 2y – 4 = 0 by determinant method find
   D.
   (A) 5 (B) 1 (C) -5 (D) -1
   (5) ax + by = c and mx + ny = d andan 1 bm then these simultaneous equations have –
   (A) Only one common solution. (B) No solution.
   (C) Infinite number of solutions. (D) Only two solutions. 2. Complete the following table to draw the graph of 2x – 6y = 3
   x
   y0
   (x, y)
2. Solve the following simultaneous equations graphically. (1) 2x + 3y = 12 ; x – y = 1
   (2) x – 3y = 1 ; 3x – 2y + 4 = 0
   (3) 5x – 6y + 30 = 0 ; 5x + 4y – 20 = 0
   (4) 3x – y – 2 = 0 ; 2x + y = 8
   (5) 3x + y = 10 ; x – y = 2
3. Find the values of each of the following determinants.
   (C) 41
   (D) 1
   -5
   (1) 4 3 (2) 5 -2 27 -31
   (3)
   3 -1 14

5. Solve the following equations by Cramer’s method.
   (1) 6x – 3y = -10 ; 3x + 5y – 8 = 0
   (2) 4m – 2n = -4 ; 4m + 3n = 16
   (3) 3x – 2y = 52 ; 13x + 3y = -43
   (4) 7x + 3y = 15 ; 12y – 5x = 39
   x  y 8 x  2y 14 3x  y 234
   (5)
6. Solve the following simultaneous equations.
   (1) 2  2 1 ; 3  2 0 (2) 7  13 27 ; 13  7 33 x3y6xy 2x1y22x1y2
   (3) 148  231 527 ; 231  148 610 (4) 7x2y 5 ; 8x7y 15 x y xy x y xy xy xy
   (5) 1  1 1 ; 5  2 3 2(3x4y) 5(2x3y) 4 (3x4y) (2x3y) 2
7. Solve the following word problems.
   (1) A two digit number and the number with digits interchanged add up to 143. In the given number the digit in unit’s place is 3 more than the digit in the ten’s place. Find the original number.
   Let the digit in unit’s place is x
   and that in the ten’s place is y
   \ the number = y + x
   The number obtained by interchanging the digits is x + y
   According to first condition two digit number + the number obtained by interchanging the digits = 143
   \ +=143 \ x + y = 143
   x + y = . . . . . (I) From the second condition,
   digit in unit’s place = digit in the ten’s place + 3 \x= +3
   \ x – y = 3 . . . . . (II) Adding equations (I) and (II)

2x =
Putting this value of x in equation (I) x + y = 13
8+ =13 \y=
The original number is 10 y + x =+8
=58 1
(2) Kantabai bought 1 2 kg tea and 5 kg sugar from a shop. She paid 50 as return fare for rickshaw. Total expense was 700. Then she realised that by ordering online the goods can be bought with free home delivery at the same price. So next month she placed the order online for 2 kg tea and 7 kg sugar. She paid 880 for that. Find the rate of sugar and tea per kg. (3) To find number of notes that Anushka had, complete the following activity. \ The No. of notes ( , ) (4) Sum of the present ages of Manish and Savita is 31. Manish’s age 3 years ago  was 4 times the age of Savita. Find their present ages. (5) In a factory the ratio of salary of skilled and unskilled workers is 5 : 3. Total salary of one day of both of them is 720. Find daily wages of skilled and
unskilled workers.
(6) Places A and B are 30 km apart and they are on a straight road. Hamid travels from A to B on bike. At the same time Joseph starts from B
on bike, travels towards A. They meet each other after 20
minutes. If Joseph would have started from B at the same
time but in the opposite direction (instead of towards A) Hamid would have caught him after 3 hours. Find the speed
x=8
Suppose that Anushka had x notes of 100 and y notes of 50 each
If Anand would have given her the amount by interchanging number of notes, Anushka would have received 500 less than the previous amount \ .............. equation II Anushka got 2500/- from Anand as denominations mentioned above \ …………. equation I
of Hamid and Joseph.

Problem-Set-1-Part-A Problem-Set-1-Part-B