Solve the following pair of linear equations:
$119 x - 381 y = 643$ ; $381 x - 119 y = - 143$

x = - 1

and

y = - 2

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x = 8

and

y = - 1

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x = 3

and

y = 5

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x = 7

and

y = - 9

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Solution

The correct option is A $x = - 1$ and $y = - 2$
The given equations are
$119 x - 381 y$ $=$ $643$ ....(1)
$381 x - 119 y$ $=$ $- 143$ .....(2)
Adding equations (1) and (2), we get
$500 x - 500 y$ $=$ $500$
$x - y$ $=$ $1$ .......(3)
Subtracting equation (2) from (1), we get
$262 x - 262 y$ $=$ $786$
$x + y$ $=$ $- 3$ ......(4)
Adding equations (3) and (4)
$2 x$ $=$ $- 2$
$x$ $=$ $- 1$
Putting value of $x$ $=$ $- 1$ in equation (4), we get
$- 1 + y$ $=$ $= - 3$
$y = - 2$
Hence $x$ $=$ $- 1$ and $y$ $=$ $- 2$ .

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