Solve for x, y and z? (5xy)/(x+y)=6

Guillermo May

Guillermo May

Answered question

2023-02-04

Solve for x, y and z?
5 x y x + y = 6

Answer & Explanation

Melaniqk2

Melaniqk2

Beginner2023-02-05Added 5 answers

We have:
{ 5 x y x + y = 6 4 x z x + z = 3 3 y z y + z = 2
Multiplying both sides of the first equation by x + y x y , the second equation by 2 x + z x z and the third by 3 y + z y z we get:
{ 5 = 6 ( 1 x ) + 6 ( 1 y ) 8 = 6 ( 1 x ) + 6 ( 1 z ) 9 = 6 ( 1 y ) + 6 ( 1 z )
The following results are obtained by substituting the third equation for the second equation in the final two equations:
{ 5 = 6 ( 1 x ) + 6 ( 1 y ) - 1 = 6 ( 1 x ) - 6 ( 1 y )
When these two equations are combined, we obtain:
4 = 12 ( 1 x )
Hence x=3
Then:
6 ( 1 y ) = 5 - 6 ( 1 x ) = 5 - 2 = 3
Hence y=2
Then:
6 ( 1 z ) = 9 - 6 ( 1 y ) = 9 - 3 = 6
Hence z=1

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?