Question

If 3x + i(4x-y) = 6-i, where x and y are real numbers, then the value of x and y are respectively

• A. 3,9
• B. 2,9
• C. 2,4
• D. 3,4

Answer 1

The Correct Option is B

To find the values of x and y in the equation \(3x + i(4x - y) = 6 - i\), we can equate the real and imaginary parts on both sides of the equation.
Equating the real parts:
3x = 6
Dividing both sides by 3, we get:
x = 2
Equating the imaginary parts:
\(i(4x - y) = -i\)
Multiplying both sides by -i, we get:
\(4x - y = -1\)
Substituting the value of x from the first equation, we have:
\(4(2) - y = -1\)
\(8 - y = -1\)
Subtracting 8 from both sides, we get:
\(-y = -9\)
Dividing both sides by -1, we get:
y = 9
Therefore, the values of x and y in the equation \(3x + i(4x - y) = 6 - i\) are x = 2 and y = 9 (option B).

Answer 2

We are given a complex equation:  
\[ 3x + i(4x - y) = 6 - i \] 
Here, both sides of the equation are complex numbers. For two complex numbers to be equal, their real parts and imaginary parts must be equal.

Step 1: Equate the real parts: \[ 3x = 6 \Rightarrow x = \frac{6}{3} = 2 \]

Step 2: Equate the imaginary parts: \[ 4x - y = -1 \] Substitute \(x = 2\): \[ 4(2) - y = -1 \Rightarrow 8 - y = -1 \Rightarrow y = 9 \]
Final Answer: x = 2, y = 9 
Correct option: 2, 9

Answer 3

We are given the equation 3x + i(4x - y) = 6 - i, where x and y are real numbers.

For two complex numbers to be equal, their real parts must be equal, and their imaginary parts must be equal.

Equating the real parts:

3x = 6

x = 6 / 3

x = 2

Equating the imaginary parts:

4x - y = -1

Substitute the value of x (x = 2) into the second equation:

4(2) - y = -1

8 - y = -1

y = 8 + 1

y = 9

Therefore, x = 2 and y = 9.

Answer:

2,9