Solve each of the following systems of equations by using the method of cross multiplication:

$6 x - 5 y - 16 = 0, 7 x - 13 y + 10 = 0.$

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Solution

$6 x - 5 y - 16 = 0$ -----(1)

$7 x - 13 y + 10 = 0$ ----- (2)

By cross multiplication, we have

$\frac{x}{[- 5 \times 10 - (- 16) \times (- 13)]} = \frac{y}{[(- 16 \times 7) - 10 \times 6]} = \frac{1}{[6 \times (- 13) - (- 5) \times 7]} \Rightarrow \frac{x}{(- 50 - 208)} = \frac{y}{(- 112 - 60)} = \frac{1}{(- 78 + 35)} \Rightarrow \frac{x}{- 258} = \frac{1}{- 43}, \frac{y}{- 172} = \frac{1}{- 43} \Rightarrow x = \frac{- 258}{- 43} = 6, y = \frac{- 172}{- 43} = 4$

Hence, x = 6 and y = 4 is the solution.

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