Engineering Mechanics - General Principles - Discussion
Discussion Forum : General Principles - General Questions (Q.No. 4)
4.
Solve the following equation for x, y, and z:
x – y + z = –1 –x + y + z = –1 x + 2y – 2z = 5
Discussion:
14 comments Page 1 of 2.
K.devika said:
1 decade ago
@Karthik is correct.
(1)
Karthik said:
1 decade ago
Substitute each value un the equation whichever satisfies the equation is the answer.
Arpita majumder said:
1 decade ago
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
=>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:
1 decade ago
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
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:
1 decade ago
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
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:
1 decade ago
I go with both Manpreet, Samarth Patel because both are right.
Vikas mishra said:
1 decade ago
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.
Hamid said:
1 decade ago
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.
-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:
1 decade ago
Substitute each value in the equation whichever satisfies the equation is the answer.
Nayan said:
1 decade ago
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.
-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.
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