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Consider the system x + y + z = 0; x - y - z = 0, then the system of equations have
- a)no solution
- b)infinite solution
- c)unique solution
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Consider the system x + y + z = 0; x - y - z = 0, then the syst...
We are given that the system of equation,
x + y + z = 0
x - y - z = 0
This system of equations has rank 2 and 3 unknowns,
that is, rank < no. of unknown
Hence, this system of equation has infinitly many solution.
x + y + z = 0
x - y - z = 0
This system of equations has rank 2 and 3 unknowns,
that is, rank < no. of unknown
Hence, this system of equation has infinitly many solution.
Most Upvoted Answer
Consider the system x + y + z = 0; x - y - z = 0, then the syst...
Given information:
The given system of equations is:
1) x + y + z = 0
2) x - y - z = 0
To determine:
The type of solution for the given system of equations.
Solution:
To determine the type of solution for the given system of equations, we can use the method of elimination or substitution.
Method of elimination:
We can eliminate one variable by adding or subtracting the equations. Let's eliminate the variable z.
Adding equation 1 and equation 2, we get:
(x + y + z) + (x - y - z) = 0 + 0
2x = 0
x = 0
Substituting x = 0 in equation 1, we get:
0 + y + z = 0
y + z = 0
y = -z
So, the solution to the system of equations is x = 0, y = -z, where z can be any real number.
Explanation:
The given system of equations represents a plane in three-dimensional space. The equations represent the intersection of two planes. In this case, the planes intersect along a line. Therefore, the system of equations has infinitely many solutions.
Answer:
The system of equations has infinite solutions (option B).
The given system of equations is:
1) x + y + z = 0
2) x - y - z = 0
To determine:
The type of solution for the given system of equations.
Solution:
To determine the type of solution for the given system of equations, we can use the method of elimination or substitution.
Method of elimination:
We can eliminate one variable by adding or subtracting the equations. Let's eliminate the variable z.
Adding equation 1 and equation 2, we get:
(x + y + z) + (x - y - z) = 0 + 0
2x = 0
x = 0
Substituting x = 0 in equation 1, we get:
0 + y + z = 0
y + z = 0
y = -z
So, the solution to the system of equations is x = 0, y = -z, where z can be any real number.
Explanation:
The given system of equations represents a plane in three-dimensional space. The equations represent the intersection of two planes. In this case, the planes intersect along a line. Therefore, the system of equations has infinitely many solutions.
Answer:
The system of equations has infinite solutions (option B).
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Community Answer
Consider the system x + y + z = 0; x - y - z = 0, then the syst...
We are given that the system of equation,
x + y + z = 0
x - y - z = 0
This system of equations has rank 2 and 3 unknowns,
that is, rank < no. of unknown
Hence, this system of equation has infinitly many solution.
x + y + z = 0
x - y - z = 0
This system of equations has rank 2 and 3 unknowns,
that is, rank < no. of unknown
Hence, this system of equation has infinitly many solution.
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Consider the system x + y + z = 0; x - y - z = 0, then the system of equations havea)no solutionb)infinite solutionc)unique solutiond)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
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