Matrices & Determinants
System of Linear Equations
Grade 12
Question:
<p>The number of values of \(k\) for which the system of equations<br/>\((k+1)x + 8y = 4k\)<br/>\(kx + (k+3)y = 3k - 1\)<br/>has no solution, is</p>
<p>(a) 1</p>
<p>(b) 2</p>
<p>(c) 3</p>
<p>(d) infinite</p>
Step-by-Step Solution
Key Concept: A system of linear equations has no solution when the coefficient determinant is zero but the system is inconsistent.
<p><strong>Solution:</strong> A system has no solution when the lines are parallel but not coincident. This occurs when the determinant of coefficients is zero but the determinant with augmented column is non-zero.</p>
Correct Answer: A