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Example     Solve 3 x - 5 y = 16; x - 3 y = 8

Solution:     3 x - 5 y = 16 . . . (1)

x - 3 y = 8 . . . (2)

To make the coefficients of x equal,

by multiplying the equation (2) by 3 we get

3 x - 9 y = 24 . . . (3)

For eliminating x, subtract equation (3) from (1)

3 x - 5 y = 16 . . . (1)

3 x - 9 y = 24 . . . (3)

(-) (+) (-)

4 y = - 8

y = - 2

Inserting y = -2 in (1), (2) or (3). But it is convenient to insert this value in equation (2)

\ x - 3 (-2) = 8

\ x + 6 = 8

\x = 8 - 6

\x = 2

Therefore, x = 2, y = -2 is the required option.

Example     Solve 2 x - 3 y = 14; 5 x + 2 y = 16

Solution:     2 x - 3 y = 14 . . . (1)

5 x + 2 y = 16 . . . (2)

If we multiply (1) by 2 and (2) by 3 the coefficients of y will be numerically equal

By multiplying (1) by 2; 4 x - 6 y = 28 . . . (3)

By multiplying (2) by 3; 15 x + 6 y = 48 . . . (4)

Adding (3) and (4), y will be eliminated as

19 x = 76

\ x = 4

Inserting x = 4 in (2) we get

Therefore, x = 4, y = -2 is the solution

Index

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

Chapter 8

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