Question

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

Answer 1

Step-by-step explanation:

To find the values of x and y in the equation 4x + i(3x - y) = 3 +i(-6), we can separate the real and imaginary parts of the equation.

Step 1: Separate the real and imaginary parts.

The real part of the equation is 4x and the imaginary part is i(3x - y).

Step 2: Equate the real parts and imaginary parts separately.

Equating the real parts, we have:

4x = 3

Equating the imaginary parts, we have:

3x - y = -6

Step 3: Solve the equations.

From the first equation, we can solve for x:

4x = 3

Divide both sides by 4:

x = 3/4

Substitute x = 3/4 into the second equation and solve for y:

3(3/4) - y = -6

Multiply 3/4 by 3:

9/4 - y = -6

Move y to the left side:

-y = -6 - 9/4

Combine like terms:

-y = -24/4 - 9/4

Simplify:

-y = -33/4

Multiply both sides by -1 to isolate y:

y = 33/4

Therefore, the values of x and y that satisfy the equation are x = 3/4 and y = 33/4.

Answer 2

To solve for x and y in equation 4x + i(3x - y) = 3 +i (-6), we equate the real and imaginary parts to get two separate equations: 4x = 3 and 3x - y = -6. Solving these gives us x = 3/4 and y = 33/4.

Step-by-step explanation:

To find the values of x and y from the equation 4x + i(3x - y) = 3 +i (-6), we first recognize that we are dealing with a complex equation. Both sides of the equation have a real part and an imaginary part. We can equate the real parts and the imaginary parts separately to solve for the variables.

The real parts of the equation are: 4x = 3, and the imaginary parts are: 3x - y = -6. By solving these two equations simultaneously, we can determine the values for x and y.

Firstly, solve the real part:

1. 4x = 3
2. x = 3/4

Then solve the imaginary part using the value of x we just found:

1. 3x - y = -6
2. 3*(3/4) - y = -6
3. 9/4 - y = -6
4. -y = -6 - 9/4
5. -y = -24/4 - 9/4
6. -y = -33/4
7. y = 33/4

The final values are x = 3/4 and y = 33/4.