Solve the system of equations $2 x + 3 y = 17, 3 x - 2 y = 6$ by the method of cross multiplication.

x = 4, y = 3

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x = 5, y = 3

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x = 4, y = 4

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None of these

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Solution

The correct option is A $x = 4, y = 3$
By cross multiplication method
$x = \frac{(b_{1} c_{2} - b_{2} c_{1})}{(a_{1} b_{2} - a_{2} b_{1})}$ &
$y = \frac{(c_{1} a_{2} - c_{2} a_{1})}{(a_{1} b_{2} - a_{2} b_{1})}$
Where $a_{1} x + b_{1} y + c_{1} = 0$ & $a_{2} x + b_{2} y + c_{2} = 0$
are $2$ lines
$\Rightarrow x = \frac{3 (- 6) - (- 2) (- 17)}{2 (- 2) - (3 \times 3)} = \frac{- 52}{- 13} = 4$
$y = \frac{(- 17) 3 - (- 6) 2}{2 (- 2) - (3 \times 3)} = \frac{- 39}{- 13} = 3$
$\Rightarrow x = 4 & y = 3$

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