Question

Find x and y if (x+2y)+(2x-3y) is the conjugate of 5+4i

Answer 1

Answer:

The value of x and y is $x=\frac{23}{7}$ and $y=\frac{6}{7}$

Step-by-step explanation:

Given : If (x+2y)+(2x-3y)i is the conjugate of 5+4i.

To find : The value of x and y?

Solution :

If (x+2y)+(2x-3y) is the conjugate of 5+4i.

i.e. $(x+2y)+(2x-3y)i=5+4i$

On comparing,

$x+2y=5$....(1) and $2x-3y=4$.....(2)

Solving the equations,

Multiply (1) by 2 and subtract from (2),

$2x-3y-2x-4y=4-10$

$-7y=-6$

$y=\frac{6}{7}$

Substitute the value of y in equation (1),

$x+2(\frac{6}{7})=5$

$x+\frac{12}{7}=5$

$7x+12=35$

$7x=23$

$x=\frac{23}{7}$

Therefore, The value of x and y is $x=\frac{23}{7}$ and $y=\frac{6}{7}$