Which one is correct, the following system of linear equations 2x – 3y + 4z = 7, 3x – 4y + 5z = 8, 4x – 5y + 6z = 9 has?a)No solutionsb)Infinitely many solutionsc)Unique Solutiond)Can’t be predictedCorrect answer is option 'B'. Can you explain this answer?

Question

Which one is correct, the following system of linear equations 2x &ndash; 3y + 4z = 7, 3x &ndash; 4y + 5z = 8, 4x &ndash; 5y + 6z = 9 has?a)No solutionsb)Infinitely many solutionsc)Unique Solutiond)Can&rsquo;t be predictedCorrect answer is option 'B'. Can you explain this answer?

Answer

Solving the given system of equation by Cramer’s rule, we get,
x = D₁/D, y = D₂/D, z = D₃/D where,

Now, performing, C₃ = C₃ – C₂ and C₂ = C₂ – C₁ we get,

As two columns have identical values, so,
D = 0
Similarly,

Now, performing, C₁ = C₁– C₃

Now, performing, C₃ = C₃– C₂

As two columns have identical values, so,
D₁ = 0

Now, performing,

Now, performing, C₂ = C₂ – C₃ and C₃ = C₃ – C₁

As two columns have identical values, so,
D₂ = 0

Now, performing, C₂ = C₂ – C₂ and C₃ = C₃ – C₂

As two columns have identical values, so,
D₃ = 0
Since, D = D₁ = D₂ = D₃= 0, thus, it has infinitely many solutions.

Answer

It seems that you have not completed the statement of the system of linear equations. Please provide the complete equations so that I can determine which one is correct.

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