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Find the value of  a so that the system has no solutions.

 

y = 11x + 14

2x - 4 = ax + 7 - 3x

 Feb 25, 2021
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The system is equivalent to

 

\(\begin{bmatrix}11&-1\\a-5&0\end{bmatrix} \begin{bmatrix}x\\y\end{bmatrix} = \begin{bmatrix}-14\\-11\end{bmatrix}\)

 

The system has no solutions when the determinant of \(\begin{bmatrix}11&-1\\a-5&0\end{bmatrix}\) is 0.

 

\(\det \begin{bmatrix}11&-1\\a-5&0\end{bmatrix} = 0\\ -(a - 5) = 0\\ \boxed{a = 5}\)

 

Therefore, the system has no solutions when a = 5.

 Feb 25, 2021

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