Solve the equations using cross multiplication method: $x - y = 12$ and $x + y = 14$

x = 13, y = 1

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x = 13, y = - 1

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x = - 13, y = - 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x = - 13, y = 1

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Solution

The correct option is C $x = 13, y = 1$
$x - y = 12$ ---(1)
$x + y = 14$ ---(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 $c$ .
$\frac{x}{- 1 \times 14 - 1 \times 12} = \frac{y}{12 \times 1 - 1 \times 14} = \frac{- 1}{1 \times 1 - 1 \times (- 1)}$
$\frac{x}{- 14 - 12} = \frac{y}{12 - 14} = \frac{- 1}{1 + 1}$
$\frac{x}{- 26} = \frac{y}{- 2} = \frac{- 1}{2}$
$\frac{x}{- 26} = \frac{- 1}{2}$
$2 x = 26$
$x = 13$
$\frac{y}{- 2} = \frac{- 1}{2}$
$2 y = 2$
$y = 1$
Therefore, $x = 13, y = 1$

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