Using cross multiplication find the value of $x$ and $y$ for the equations:
$15 x + 11 y = - 23$ and $- 2 x + 7 y = 20$

x = - 3, y = 2

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x = 0, y = 2

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x = - 3, y = - 2

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x = 0, y = 0

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Solution

The correct option is A $x = - 3, y = 2$
$15 x + 11 y = - 23$ ---(1)
$- 2 x + 7 y = 20$ ---(2)
Using formula for cross multiplication method:
$\frac{x}{(b_{1} c_{2} - b_{2} c_{1})} = \frac{y}{(c_{1} a_{2} - a_{1} c_{2})} = \frac{- 1}{(a_{1} b_{2} - a_{2} b_{1})}$
So, from equation (1) and (2) we can write the value of $a, b$ and $c$ .
$\frac{x}{11 \times 20 - 7 \times - 23} = \frac{y}{(- 23) \times (- 2) - 15 \times 20} = \frac{- 1}{15 \times 7 - (- 2) \times 11}$
$\frac{x}{220 + 161} = \frac{y}{46 - 300} = \frac{- 1}{105 + 22}$
$\frac{x}{381} = \frac{y}{- 254} = \frac{- 1}{127}$
$\frac{x}{381} = \frac{- 1}{127}$
$127 x = - 381$
$x = - 3$
$\frac{y}{- 254} = \frac{- 1}{127}$
$127 y = 254$
$y = 2$
Therefore, $x = - 3, y = 2$

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