Question 65601
QUESTION:


Solve

x + y + z = 11
2x + y - z = 13
x = 2y


ANSWER:

x + y + z = 11   -----------------------(1)


2x + y - z = 13  -----------------------(2)


x = 2y   -------------------------------(3)




Fron (2) we have, x = 2y. 




Substitute this value in (1) and (2)




==>
2y + y + z = 11  
 



3y + z = 11      ------------------------(4)



2(2y) + y - z = 13  



4y + y - z = 13




==> 5y - Z = 13 -------------------------(5)




Let's take (4) and (5) together,





3y + z = 11      ------------------------(4)




5y - Z = 13      ------------------------(5)


_____________________________________________________________________________


Add (4) and (5) ====>



3y + z + 5y - Z = 11  + 13




==> 8y = 24



Divide both sides by 8,




==> 8y/8 = 24/8




==> y = 3




Substitute the value of y in equation (3) x = 2y





==> x = 2* 3




==> x = 6




    
Input the values of x and y in equation (1)




6 + 3 + z = 11

   


==> 9 + z = 11




Subtract 9 from both sides,




==> 9 + z - 9 = 11 - 9 




==> z = 2 




so the solution is,




x = 6

y = 3

z = 2





Hope you understood.



Regards.


praseenakos@yahoo.co.in