Question

- (x + 3y)i + (2x – y + 1)=8\i

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Answer 1

SOLUTION

GIVEN

$\displaystyle\sf{ - (x + 3y)i + (2x - y + 1) = \frac{8}{i} }$

TO DETERMINE

The value of x and y

EVALUATION

Here it is given that

$\displaystyle\sf{ - (x + 3y)i + (2x - y + 1) = \frac{8}{i} }$

$\displaystyle\sf{ \implies \: - (x + 3y)i + (2x - y + 1) = \frac{8i}{ {i}^{2} } }$

$\displaystyle\sf{ \implies \: - (x + 3y)i + (2x - y + 1) = \frac{8i}{ - 1} }$

$\displaystyle\sf{ \implies \: - (x + 3y)i + (2x - y + 1) = - 8i }$

Comparing both sides we get

2x - y + 1 = 0 - - - - - - (1)

x + 3y = 8 - - - - - - - (2)

From Equation 1 we get

y = 2x + 1

From Equation 2 we get

x + 6x + 3 = 8

⇒ 7x = 5

$\displaystyle\sf{ \implies \:x = \frac{5}{7} }$

Thus we get

$\displaystyle\sf{ y = \frac{10}{7} + 1 = \frac{17}{7} }$

FINAL ANSWER

$\displaystyle\sf{ x = \frac{5}{7} \: \: and \: \: y = \frac{17}{7} }$

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