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.
Manohar h s said:
6 years ago
I didn't understand this. Please, anyone, explain me.
Venkatesh said:
8 years ago
Solve by Cramer's rule (matrix method).
@zikky90 said:
9 years ago
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.
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.
Mohit said:
9 years ago
@Karthik. Your method is wrong for solving the problem because if you putting the values of option D then you also get equal equations.
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.
Shaikh mosin ahmed said:
1 decade ago
Substitute each value in the equation whichever satisfies the equation is the answer.
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.
K.devika said:
1 decade ago
@Karthik is correct.
(1)
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.
Damodaran said:
1 decade ago
I go with both Manpreet, Samarth Patel because both are right.
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