Solve The Following System Of Equations By Elimination Method: 8X - 3Y = 5XY, 6X - 5Y = -2XY. X = Y ≠ 0.

Consider the given equations.

8x −3y = 5xy — [1]

6x − 5y = −2xy —[2]

From both the equation: [1] and [2]

Now by multiplying the equation [1] by 6 and equation [2] by 8, we get:

48x + 18y = 30xy

48x – 40y = -16xy

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22y  = 46xy

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X = \(\frac{11}{23} \)

Now by substituting the value of x in the equation [2], we get

\(6 * \frac{11}{23} – 5y = -2 * \frac{11}{23}y \\\Rightarrow \frac{66 – 115y}{23} = \frac{22}{23} y\\\Rightarrow 66 – 115y = – 22y \\\Rightarrow 93y = 66 \\\Rightarrow y = \frac{66}{93} \\\Rightarrow y = \frac{22}{31} \)

Therefore,

The value of x is \( \frac{11}{23}\)

The value of y is  \( \frac{22}{31} \)

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