i don't understand how to solve this system ?

[adamhejazy]

 

[Deleted member 4993]

Your images are too small to see properly.

However, it looks like you have 3 equations with 3 unknowns (with complex coefficients).

Where are you stuck exactly?

Please share your work with your question.

 

[adamhejazy]

 

[adamhejazy]

sorry for late reply !

Your images are too small to see properly.

However, it looks like you have 3 equations with 3 unknowns (with complex coefficients).

Where are you stuck exactly?

Please share your work with your question.

Y=X+Z
X*15.8 - Z*6.819e^-j13˚ =8.485e^j12˚
Y*6.819e^-j13˚ + Z*3.675e^j90˚ = 7,071e^j12˚

x=?
y=?
z=?

 

[HallsofIvy]

Y=X+Z
X*15.8 - Z*6.819e^-j13˚ =8.485e^j12˚
Y*6.819e^-j13˚ + Z*3.675e^j90˚ = 7,071e^j12˚

x=?
y=?
z=?

Better! But so it won't be so hard to type, I am going to write A= 15.8, B= 6.819e^-13j, C= 8.485e^12j, D= 3.675e^90j, and E= 7,071e^12j.
The equations are Y= X+ Z, AX- BZ= C, and BY+ DZ= E. Since Y= X+ Z, the third equation can be written B(X+ Z)+ Dz= BX+ (B+ D)Z= E.
So we have AX- BZ= C and BX+ (B+ D)Z= E. Multiply the first equation by B+ D and the second equation by B to get
A(B+ D)X- B(B+ D)Z= C(B+ D) and
B^2X+ B(B+ D)Z= BE.

Adding those equations eliminates Z: (A(B+ D)+ B^2)X= C(B+D)+ BE.

By the way, your solutions are "X= , Y= , Z= " not "x= , y= , z= ".