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Example      Solve 15 x + 17 y = 21; 17 x + 15 y = 11

Solution:     15x + 17y = 21 . . . (1)

17x + 15y = 11 . . . (2)

The work in these equations would be laborious if we tried to eliminate x or y by making their coefficients equal. We notice, however, that if we add (1) and (2), we have

15 x + 17 y = 21 . . . (1)

17 x + 15 y = 11 . . . (2)

32 x + 32 y = 32

Dividing by 32 throughout,

x + y = 1 . . . (3)

Again, by subtracting (2) from (1), we have

17 x + 15 y = 11

15 x + 17 y = 21

(-) (-) (-)

2 x - 2 y = -10

Dividing by 2 throughout,

x - y = -5 . . . (4)

Adding (3) and (4)

x + y = 1

x - y = -5

2 x = -4

x = -2 and

Subtracting (4) from (3)

x + y = 1

x - y = -5

(-) (+) (+)

2 y = 6

y = 3

Therefore, x = -2, y = 3 is the required solutions.

Index

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

Chapter 8

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