+0

# system

0
81
1

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

y = 11x + 14

2x - 4 = ax + 7 - 3x

Feb 25, 2021

#1
+8455
0

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