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The solution of equations $x - 3 y = 8$ and $x - 9 y = 14$ is

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x = - 5

and

y = - 1

x = 5

and

y = 1

x = - 5

and

y = 1

x = 5

and

y = - 1

answer is D.

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Detailed Solution

x - 3 y = 8

and

x - 9 y = 14

Comparing with

a_{1} x + b_{1} y + c_{1} = 0

and

a_{2} x + b_{2} y + c_{2} = 0

, we get

a_{1} = 1,

b_{1} = - 3

and

c_{1} = - 8

a_{2} = 1,

b_{2} = - 9

and

c_{2} = - 14

By cross-multiplication formula, we have

\frac{x}{b_{1} c_{2} - b_{2} c_{1}} = \frac{y}{c_{1} a_{2} - a_{1} c_{2}} = \frac{1}{b_{2} a_{1} - a_{2} b_{1}}

\frac{x}{(- 3) (- 14) - (- 9) (- 8)} = \frac{y}{(- 8) (1) - (1) (- 14)} = \frac{1}{(- 9) (1) - (1) (- 3)}

\frac{x}{42 - 72} = \frac{y}{- 8 + 14} = \frac{1}{- 9 + 3}

\frac{x}{- 30} = \frac{y}{6} = \frac{1}{- 6}

x = \frac{- 30}{- 6}

and

y = \frac{6}{- 6}

x = 5

and

y = - 1

Therefore, 4 is the correct option.

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