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Consider the following system of equations in three real variables x, y, z.
2x – 3y + 7z = 5
3x + y – 3z = 13
2x + 19y – 47z = 32
The system of the equation has
  • a)
    No solution
  • b)
    A unique solution
  • c)
    More than one but a finite number of solutions
  • d)
    An infinite number of solutions
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Consider the following system of equations in three real variables x, ...
Augmented matrix will be
R3 → R3 – R1
R2 → 2R2 – 3R1

R3 → R3 – 2R2

 
Rank of A ≠ Rank of Augmented matrix
Hence given system of equations has no solution.
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Most Upvoted Answer
Consider the following system of equations in three real variables x, ...
+ 3y - z = 5
x - 4y + 2z = -7
3x + y - 3z = 2

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:

From the first equation, we can express z in terms of x and y:
z = 2x + 3y - 5

Now, we substitute z in the other two equations:

x - 4y + 2(2x + 3y - 5) = -7
3x + y - 3(2x + 3y - 5) = 2

Simplify these equations:

x - 4y + 4x + 6y - 10 = -7
3x + y - 6x - 9y + 15 = 2

Combine like terms:

5x + 2y = 3
-3x - 8y = -13

Now we can solve this system of equations using substitution or elimination to find the values of x, y, and z.
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Consider the following system of equations in three real variables x, y, z.2x – 3y + 7z = 53x + y – 3z = 132x + 19y – 47z = 32The system of the equation hasa)No solutionb)A unique solutionc)More than one but a finite number of solutionsd)An infinite number of solutionsCorrect answer is option 'A'. Can you explain this answer?
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