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
