The real values of x and y for which the equa | vedclass

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(C) Given equation: $(x + iy)(2 - 3i) = 4 + i$Expanding the left side: $(2x + 3y) + i(-3x + 2y) = 4 + i$Equating real and imaginary parts:$2x + 3y = 4

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$x = \frac{5}{13}, y = \frac{14}{13}$

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(C) Given equation: $(x + iy)(2 - 3i) = 4 + i$Expanding the left side: $(2x + 3y) + i(-3x + 2y) = 4 + i$Equating real and imaginary parts:$2x + 3y = 4$ ... $(i)$$-3x + 2y = 1$ ... $(ii)$Multiplying $(i)$ by $3$ and $(ii)$ by $2$:$6x + 9y = 12$$-6x + 4y = 2$Adding the two equations: $13y = 14 \implies y = \frac{14}{13}$Substituting $y$ in $(i)$: $2x + 3(\frac{14}{13}) = 4 \implies 2x = 4 - \frac{42}{13} = \frac{52 - 42}{13} = \frac{10}{13} \implies x = \frac{5}{13}$Thus,$x = \frac{5}{13}$ and $y = \frac{14}{13}$.

The real values of $x$ and $y$ for which the equation $(x + iy)(2 - 3i) = 4 + i$ is satisfied,are

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