Engineering Mechanics - General Principles - Discussion

Discussion :: General Principles - General Questions (Q.No.4)

4. 

Solve the following equation for x, y, and z:

xy + z = –1   –x + y + z = –1   x + 2y – 2z = 5

[A]. x = 1,      y = 1,      z = –1
[B]. x = 5/3,      y = 7/6,      z = –1/2
[C]. x = –2/3,      y = –2/3,      z = –1
[D]. x = –1,      y = 1,      z = 1

Answer: Option A

Explanation:

No answer description available for this question.

Karthik said: (Dec 5, 2010)  
Substitute each value un the equation whichever satisfies the equation is the answer.

Arpita Majumder said: (Jan 3, 2011)  
x-y+z=-1
=>x-y-1+x-y=-1(putting value of z fm 2nd eqn0
=>2(x-y)=0
=>x=y
putting x=y in 1st eqn
=>z=-1
putting x=y in 3rd eqn
=>3x-2z=5
=>x=1(z=-1)
as x=1,y=1
hence,x=1,y=1 & z=-1

Manpreet said: (Feb 19, 2011)  
First you should put x & y =0
then 0 + z = -1
z = -1
put this in 1 equation
it wil x - y = 0
x = y
put this in 3 equation
x + 2x - 2(-1) = 5
3x + 2 = 5
3x = 3
x = 1 so answer is x = 1 y = 1 z = -1

Samarth Patel said: (Jun 16, 2011)  
First 2 equ
x-y+z=-1
-x+y+z=-1 solve this equ we get the value of z=-1,

now wesolve the last 2 equ and we get the value of y=1,

and last we can add the value of y & z in any equ, we can get the x=1 so that we can solve this
x=1,y=1,z=-1

Damodaran said: (Aug 13, 2011)  
I go with both Manpreet, Samarth Patel because both are right.

Vikas Mishra said: (Mar 9, 2012)  
On adding eq. 1&2 we get value of z after finding value of now we add eq 2&3 and putting the value of z and we find the value of why and then we put the value of why &z in eq 1 we find the value of x hence answer is a.

K.Devika said: (Aug 31, 2012)  
@Karthik is correct.

Hamid said: (Jun 21, 2013)  
x - y + z = -1
-x = -y + z + 1
-x= -1 + (-1) + 1
-x= -1.
Minus cancel we get x.
____________________
-x + y + z = -1
-y = -x + z + 1
-y = -1 + (-1) + 1
-y = -2 + 1 = -1
-y = -1.
Like x , We cancel minus to get y.
_____________________
x + 2y - 2z = 5
2z = x + 2y -5
2z = 1 + (2*1) -5
2z = 3 - 5
z = -2/2 = -1.

Shaikh Mosin Ahmed said: (Jan 13, 2015)  
Substitute each value in the equation whichever satisfies the equation is the answer.

Nayan said: (Apr 21, 2015)  
x-y+z = -1.
-x+y+z = -1.
---------------

2z = -2 (Minus cancel we get 2z).
z = -1.

(Putting the z = -1).

x +2y -2z = 5.
-x +y+z = -1.

x+2y = 5-2.
x+2y = 3.

-x+y-1 = -1.
-x+y = 0.

x+2y = 3.
-x+y = 0.
------------.
3y=3.
y=1.

Putting z = -1, y = 1, we get,

x-y+z = -1.
x = -1+1-1.
x = 1.

Therefore,

x = 1, y = 1, z = -1.

Mohit said: (Apr 12, 2016)  
@Karthik. Your method is wrong for solving the problem because if you putting the values of option D then you also get equal equations.

@Zikky90 said: (Jun 21, 2016)  
Using elimination method.

Step 1: Sum up eq (1) , (2) and (3). Leaves you with x+2y=3, therefore, x=3-2y.

Step 2: Put in value of x in step 1 into eq (3) , therefore z=-1.

Step 3: Put value of x in step 1 and z in step 2 into eq (2) , therefore y=1.

Step 4: Put in value of why into step 1, therefore x = 1.

Answer: x=1, y=1, z=-1.

Venkatesh said: (Aug 15, 2017)  
Solve by Cramer's rule (matrix method).

Manohar H S said: (Apr 1, 2019)  
I didn't understand this. Please, anyone, explain me.

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