Solve the following pair of simultaneous equations. 7 x + y + 10 x - y = 9 8 x + y + 15 x - y = 11

Given, 7 x + y + 10 x - y = 9 . . . 1 8 x + y + 15 x - y = 11 . . . 2 Let 1 x + y = a and 1 x - y = b , then the given equation becomes, 7 a + 10 b = 8 . . . 3 8 a + 15 b = 11 . . . 4 Multiplying equation 3 by 8 and equation 4 by 7 , we get, 56 a + 80 b = 72 . . . 5 56 a + 105 b = 77 . . . 6 Subtracting equations 5 and 6 , we get, 56 a + 80 b - 56 a - 105 b = 72 - 77 - 25 b = - 5 b = - 5 - 25 = 1 5 Substituting the value of b in equation 4 , we get, 8 a + 15 × 1 5 = 11 8 a + 3 = 11 8 a = 8 a = 1 Therefore, 1 x + y = 1 and 1 x - y = 1 5 x + y = 1 and x - y = 5 Adding both the equations, we get, x + y + x - y = 5 + 1 2 x = 6 x = 3 And, x + y = 1 3 + y = 1 y = - 2 Hence, the value of x = 3 and y = - 2 .

Solve the following pair of simultaneous equations. 5 x + y + 18 x - y = 7 20 x + y - 9 x - y = 1

Given, 5 x + y + 18 x - y = 7 . . . 1 20 x + y - 9 x - y = 1 . . . 2 Let 1 x + y = a and 1 x - y = b , then the given equation becomes, 5 a + 18 b = 7 . . . 3 20 a - 9 b = 1 . . . 4 Multiplying equation 3 by 4 we get, 20 a + 72 b = 28 . . . 5 20 a - 9 b = 1 . . . 6 Subtracting equations 5 and 6 , we get, 20 a + 72 b - 20 a + 9 b = 28 - 1 81 b = 27 b = 27 81 = 1 3 Substituting the value of b in equation 4 , we get, 20 a - 9 × 1 3 = 1 20 a - 3 = 1 20 a = 4 a = 4 20 = 1 5 Therefore, 1 x + y = 1 5 and 1 x - y = 1 3 x + y = 5 and x - y = 3 Adding both the equations, we get, x + y + x - y = 5 + 3 2 x = 8 x = 4 And, x + y = 5 4 + y = 5 y = 1 Hence, the value of x = 4 and y = 1 .

E M B I B E

ICSE MATHEMATICS CLASS 9>Algebra>Chapter 5 - Simultaneous Linear Equations>EXERCISE 5A

B Nirmala Shastry Solutions for Exercise 1: EXERCISE 5A

Author:B Nirmala Shastry

B Nirmala Shastry Mathematics Solutions for Exercise - B Nirmala Shastry Solutions for Exercise 1: EXERCISE 5A

Attempt the practice questions from Exercise 1: EXERCISE 5A with hints and solutions to strengthen your understanding. ICSE MATHEMATICS CLASS 9 solutions are prepared by Experienced Embibe Experts.