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2. Method of addition and subtraction

  1. To make the number (in fact the coefficent) in front of one unknown the same in each equation, multiply one or both equations by some suitable numbers.
  2. Add or subtract the two equations as obtained in (1) to eliminate one unknown.
  3. Solve for the other unknown.
  4. Insert the value of the unknown, obtained in (3) in one of the original equation to get the other (second) unknown.

Example     Solve y + x = 24

y - x = 4

Solution:    y + x = 24 . . . (1)

y - x = 4 . . . (2)

Adding (1) and (2)

y + x = 24

y - x = 4

2 y = 28

y = 14

Inserting y = 14 in (1)

14 + x = 24

x = 10

\ x = 10 and y = 14 is the required solution.

 

Example     Solve x + 2 y = 9; 3 x - 2 y = -5

Solution :    x + 2 y = 9 . . . (1)

3 x - 2 y = -5 . . . (2)

Observe that coefficient of y in both the equations are opposite number. Hence by adding these two equations, y can be eliminated.

x + 2 y = 9

3 x - 2 y = -5

4 x = 4

x = 1

Substituting x = 1 in (1), we get 1 + 2 y = 9

and solving this equation we get y = 4.

Therefore, x = 1 and y = 4 is the required solution

Index

7.1 Definition
7.2 Simultaneous Equations
7.3 Inequations (Inequalities)
7.4 Absolute Values

Chapter 8

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