Question:
If the system of equations \(6x-2y=3\) and \(kx-y=2\) has a unique solution, then \(k\) is not equal to
If the system of equations \(6x-2y=3\) and \(kx-y=2\) has a unique solution, then \(k\) is not equal to
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A system has a unique solution when the determinant of the coefficient matrix is non-zero.
Updated On: Jul 3, 2026
- \(1\)
- \(2\)
- \(3\)
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The Correct Option is C
Solution and Explanation
Concept:
A system of two linear equations in two unknowns has a unique solution if the determinant of the coefficient matrix is non-zero.
Step 1: Write coefficient matrix. The equations are \[ 6x-2y=3 \] \[ kx-y=2 \] The coefficient matrix is \[ A=\begin{bmatrix} 6&-2 k&-1 \end{bmatrix} \]
Step 2: Find determinant. \[ \det A=6(-1)-(-2)k \] \[ =-6+2k \] \[ =2k-6 \]
Step 3: Unique solution condition. For a unique solution, \[ \det A\neq 0 \] \[ 2k-6\neq 0 \] \[ 2k\neq 6 \] \[ k\neq 3 \]
Step 4: Final answer. \[ \boxed{3} \]
A system of two linear equations in two unknowns has a unique solution if the determinant of the coefficient matrix is non-zero.
Step 1: Write coefficient matrix. The equations are \[ 6x-2y=3 \] \[ kx-y=2 \] The coefficient matrix is \[ A=\begin{bmatrix} 6&-2 k&-1 \end{bmatrix} \]
Step 2: Find determinant. \[ \det A=6(-1)-(-2)k \] \[ =-6+2k \] \[ =2k-6 \]
Step 3: Unique solution condition. For a unique solution, \[ \det A\neq 0 \] \[ 2k-6\neq 0 \] \[ 2k\neq 6 \] \[ k\neq 3 \]
Step 4: Final answer. \[ \boxed{3} \]
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