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Can someone please help me on this math problem 

 

 

Given \(\begin{align*} px+qy+rz&=1,\\ p+qx+ry&=z,\\ pz+q+rx&=y,\\ py+qz+r&=x,\\ p+q+r&=-3, \end{align*}\)FIND \(x+y+z\)

 Nov 27, 2021
 #1
avatar+115747 
+1

This question is easy.

Add the first 4 equations together

sum of left = sum of right

 you will have 

 

p( ...) +q(...) +r( ...) = (...)

 

factorize and take it from there

 Nov 27, 2021
 #2
avatar+79 
+1

SO would that simplify to \(p(x+y+z)+q(x+y+z)+r(x+y+z)=1+x+y+z\)

Jxalskdfjarkfhqwio3r  Nov 27, 2021
 #3
avatar+115747 
+1

Yes that is right.

You have, or can have   (x+y+z) four times.  Put them altogether.   

 

example

if I have   6(x+3)+m(x+3)

then I have 6 lots of x+3 and I add m lots of x+3   I end up with  6+m lots of x+3

so

6(x+3)+m(x+3) = (6+m) (x+3)

Melody  Nov 27, 2021

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