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Linear Algebra

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Moderate

Coefficients Determine the Solution

LINALG-KOGSMM

If $b$ is a real number, the linear system:

$$\begin{align*} 2x+3y&=1\\\ 4x+7y&=b\end{align*}$$

A

Is inconsistent for all $b$

B

Has infinitely many solutions, regardless of $b$

C

Has a unique solution, only when $b=\pm 1$

D

Has a unique solution for each real number $b$