Find the values of x and y in the following equation. (x + yi) + (4 + 9) = 9 -4i

(X+Yi)+(4+9i)=9-4i

The first step is removing the parenthesis:

X + Yi +4 + 9i = 9-4i 

No lets separate the like terms on both sides:

x +4 = 9
Yi +9i = -4i

We can now solve for X:  
x +4 = 9
Subtract 4 from each side:
x = 9-4
x = 5

Yi+9i = -4i

Subtract 9i from each side:
Yi = -4i-9i
Yi = -13i
Y = -13

X = 5, Y = -13.

[tex](x+yi)+(4+9i)=9-4i \\\\x+4+yi+9i=9-4i\\\\x+4+(y+9)i=9-4i\\\\x+4=9 \wedge y+9=-4\\\\x=5 \wedge y=-13 \Rightarrow \text{B}[/tex]

B. x = 5 and y = -13

Step-by-step explanation:

Equating real parts, we have ...

... x + 4 = 9

... x = 9 - 4 . . . . subtract 4

... x = 5

___

Equating imaginary parts, we have ...

... yi +9i = -4i

... yi = -4i -9i = -13i . . . . subtract 9i

... y = -13 . . . . . . . . . . . divide by i

B. x = 5 and y = -13

Step-by-step explanation:

Subtract the constant on the left:

... (x +yi) = (9 -4i) -(4 +9i)

... = (9 -4 +i(-4-9))

... = 5 -13i

Matching real and imaginary parts, we see that ...

... x = 5, y = -13

C.

Step-by-step explanation:

(x+yi)+(4+9i)=9-4i

x+yi+4+9i=9-4i

x+4+yi+9i=9-4i

Comparing the real and imaginary part we get:

x+4=9 OR y+9=-4(imaginary portion)

x=9-4 OR y=-4-9

x=5 OR y=-13

C.

y = -13

x = 5

Step-by-step explanation:

x + yi + 4 + 9i = 9 - 4i

i(9+y) + 4 + x = 9 - 4i

i(9+y) = -4i ➡ 9+y = -4 ➡ y = -13

4 + x = 9 ➡ x = 5

Step-by-step explanation:

(X+Yi)+(4+9i)=9-4i

subtract 4+9i from both sides

X + Yi = 9- 4i -(4+9i)

combine the like terms in the right side of the equation

X + Yi = 9-4 - 4i-9i

X + Yi  = 5 -13 i

Now we can compare the real part and imaginary part on both sides we get

X = 5

Y = -13

The question is incomplete. Here is the complete question:

Find the values of x and y in the following equation. (x + yi) + (4 + 9i) = 9 -4i

A.  x = 9 and y = -4

B.  x = -9 and y = 4

C.  x = 5 and y = -13

D.  x = 5 and y = 13

C. [tex]x = 5\ and\ y = -13[/tex]

Step-by-step explanation:

Given:

The equation is given as:

[tex](x + yi) + (4 + 9i) = 9-4i[/tex]

Let us combine the like terms using the commutative property of addition.

Combine the real parts together and imaginary parts together. This gives,

[tex](x+4)+(y+9)i=9-4i[/tex]

The left side of the equation is equal to the right side only if the real parts of  both the sides are equal and imaginary parts of both the sides are equal. Therefore,

[tex]x+4=9\ and\ y+9=-4\\x=9-4\ and\ y=-4-9\\x=5\ and\ y=-13[/tex]

Therefore, the values of [tex]x\ and\ y[/tex] in the given equation is [tex]x=5\ and\ y=-13[/tex]

The value of x is 15 and value of y is 18

Solution:

Given equations are:

[tex]\frac{2}{3}(x - 6) = 6\\\\\frac{2}{3}y - 6 = 6[/tex]

From first equation,

[tex]\frac{2}{3}(x - 6) = 6\\\\Remove\ the\ parenthesis\ and\ solve\\\\\frac{2}{3}x - \frac{2}{3} \times 6 = 6\\\\\frac{2}{3}x - 4 = 6\\\\Move\ the\ constant\ from\ left\ side\ to\ right\ side\\\\\frac{2}{3}x = 6 + 4\\\\\frac{2}{3}x= 10\\\\2x = 30\\\\Divide\ both\ sides\ by 2\\\\x = 15[/tex]

From second equation,

[tex]\frac{2}{3}y - 6 = 6\\\\Move\ the\ constant\ from\ left\ side\ to\ right\ side\ of\ equation\\\\\frac{2}{3}y = 6 + 6\\\\\frac{2}{3}y = 12\\\\2y = 36\\\\Divide\ both\ sides\ by\ 2\\\\y = 18[/tex]

Thus value of x is 15 and value of y is 18

We have that

if the expression is  (x + yi) + (4 + 9) = 9 -4i
x+13=9> x=9-13> x=-4
yi=-4i > y=-4

the solution is
x=-4
y=-4

if the expression has a typing error and it is really (x + yi) + (4 + 9i) = 9 -4i
then
x+4=9> x=9-4< x=5
y+9=-4> y=-4-9 > y=-13
the solution is
x=5
y=-13