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Consider the system of simultaneous equation
x + 2y + z = 6;
2x+y + 2z = 6;
x+y + z = 5
This system has
x + 2y + z = 6;
2x+y + 2z = 6;
x+y + z = 5
This system has
- a)unique solution
- b)infinite number of solution
- c)no solution
- d)exactly two solution
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Consider the system of simultaneous equationx + 2y + z = 6;2x+y + 2z =...
We are given that the system of equation
This system of equation can be written in augmented matrix as,
Applying the operations "R2 → R2 - 2R1" and "R3 → R3 - R1" these operations yields:
also applying R3 → 3R3 - R2, which yields -
Since the rank of coefficient matrix ≠ the rank of augmented matrix.
Therefore, the given system of equations has no solution.
This system of equation can be written in augmented matrix as,
Applying the operations "R2 → R2 - 2R1" and "R3 → R3 - R1" these operations yields:
also applying R3 → 3R3 - R2, which yields -
Since the rank of coefficient matrix ≠ the rank of augmented matrix.
Therefore, the given system of equations has no solution.
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Consider the system of simultaneous equationx + 2y + z = 6;2x+y + 2z =...
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Consider the system of simultaneous equationx + 2y + z = 6;2x+y + 2z =...
Explanation:
To determine the solution to the given system of simultaneous equations:
x + 2y + z = 6 ...(1)
2x + y + 2z = 6 ...(2)
x + y + z = 5 ...(3)
We can use the method of elimination or substitution to solve the system.
Method of Elimination:
To eliminate one variable, we can add or subtract the equations in a way that cancels out one variable. Let's try to eliminate the variable y.
Multiplying equation (3) by -2, we get:
-2(x + y + z) = -2(5)
-2x - 2y - 2z = -10 ...(4)
Adding equation (4) to equation (2), we have:
2x + y + 2z + (-2x - 2y - 2z) = 6 + (-10)
2x - 2x + y - 2y + 2z - 2z = -4
-y = -4
Dividing both sides by -1, we get:
y = 4 ...(5)
Substituting the value of y = 4 into equation (1), we have:
x + 2(4) + z = 6
x + 8 + z = 6
x + z = -2 ...(6)
Substituting the value of y = 4 into equation (3), we have:
x + 4 + z = 5
x + z = 1 ...(7)
Comparing equations (6) and (7), we see that they contradict each other. The left side of equation (6) is -2, whereas the left side of equation (7) is 1. Therefore, there is no solution to the given system of simultaneous equations.
Hence, the correct answer is option 'C' - no solution.
To determine the solution to the given system of simultaneous equations:
x + 2y + z = 6 ...(1)
2x + y + 2z = 6 ...(2)
x + y + z = 5 ...(3)
We can use the method of elimination or substitution to solve the system.
Method of Elimination:
To eliminate one variable, we can add or subtract the equations in a way that cancels out one variable. Let's try to eliminate the variable y.
Multiplying equation (3) by -2, we get:
-2(x + y + z) = -2(5)
-2x - 2y - 2z = -10 ...(4)
Adding equation (4) to equation (2), we have:
2x + y + 2z + (-2x - 2y - 2z) = 6 + (-10)
2x - 2x + y - 2y + 2z - 2z = -4
-y = -4
Dividing both sides by -1, we get:
y = 4 ...(5)
Substituting the value of y = 4 into equation (1), we have:
x + 2(4) + z = 6
x + 8 + z = 6
x + z = -2 ...(6)
Substituting the value of y = 4 into equation (3), we have:
x + 4 + z = 5
x + z = 1 ...(7)
Comparing equations (6) and (7), we see that they contradict each other. The left side of equation (6) is -2, whereas the left side of equation (7) is 1. Therefore, there is no solution to the given system of simultaneous equations.
Hence, the correct answer is option 'C' - no solution.
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Consider the system of simultaneous equationx + 2y + z = 6;2x+y + 2z = 6;x+y + z = 5This system hasa)unique solutionb)infinite number of solutionc)no solutiond)exactly twosolutionCorrect answer is option 'C'. Can you explain this answer?
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