Pair of Linear Equations in Two Variables Question Answers: NCERT Class 10 Mathematics

(i)                  Let the numbers be x and y, such that x > y

Therefore, according to question        

                      x - y = 26                 …………….(1)

x = 3y…………….(2)

                                   Putting the value of x from equation (2) to equation (1), we get

                                                                                    3y – y = 26

                                                                                    2y = 26

                                                                                     y = 13                  

                                    Putting the value in equation (2), we get

                                                                                     x = 3 x 13

                                                                                     x = 39   

                                    Hence, the numbers are 39 and 13.

(ii) Let one be xâ—¦ and other be yâ—¦ such that (xâ—¦ > yâ—¦)

Therefore, according to question          

                          xâ—¦ + yâ—¦ = 180â—¦…………….(1) (Supplementary angles)

xâ—¦ = 18 + yâ—¦…………….(2)

Putting the value of x from equation (2) to equation (1), we get                                             

18 + yâ—¦ + yâ—¦ = 180â—¦

2yâ—¦ = 162â—¦

Putting the value of y in equation (2), we get

                      xâ—¦ = 18 + 81

x = 99

(iv)                 Let the fixed charge be = ₨ x

Let the charge for 1 km distance be = ₨ y

According to first condition,

                                                                                   x + 10y = ₨ 105

                                                                                      x = 105 – 10y                  …………….(1)

                           According to second condition,

                                                                                     x + 15y = 155                  ………………(2) 

                                    Putting the value of x in equation (2), we get

                                                                                    105 – 10y + 15y = 155

                                                                                    5y = 50

                                                                                     y = 10 

                                    Putting the value of y in equation (2), we get

                                                                                     x + 15 x 10 = 155                               

                                                                                     x = 5

                                    Hence, the fixed charge for taxi is ₨ 5 and, the charge for one km distance is ₨ 50.

                                    Charge for 25 km distance

                                                                                     = 25 x 10 + 5

                                                                                     = ₨ 255

(vi)                 Let the age of Jacob be = x years

Let the age of Jacob’s father be = y years

After 5 years,

                                                Jacob’s age               x + 5 years

                                                   Son’s age                  y + 5 years            

                           According to question,

                       x + 5 = 3 (y + 5)           

x + 5 = 3y + 15

x = 3y + 10………………(1)

Five years ago,

(x- 5) = 7 (y - 5)

x – 5 = 7y – 35

x – 7y = -30……………….(2)

                                    Putting the value of x in equation (2), we get

                                                                                    3y + 10 - 7y = -30

                                                                                    -4y = -40

                                                                                     y = 10 

                                    Putting the value of y in equation (1), we get

                                                                                     x = 3 (10) + 10                                 

                                                                                     x = 40

                                    Hence, the present age of Jacob is 40 years and the age of his son is 10 years.

Given equations,

                            x + y + 1 = 0 …………………. (1)

                           3x + 2y + 2 = 0 ………………….. (2)

                           From the equation (1), we get

         From the equation (2), we get                

 The coordinates of vertices of triangle formed by these lines and the x- axis are (-1, 0), (4, 0), (2, 3).