Question

Determine the values of the parameter s for which the system has a unique​ solution, and describe the solution. sx 1 minus 2 sx 2sx1−2sx2 equals= 3 3 x 1 minus 6 sx 23x1−6sx2 equals= 5

Answer 1

Note: The equations written in this questions are not appropriately expressed, however, i will work with hypothetical equations that will enable you to solve any problems of this kind.

Answer:

For the system of equations to be unique, s can take all values except 2 and -2

Step-by-step explanation:

$2sx_{1} + 4x_{2} = -3\\2x_{1} + sx_{2} = 4$

$\left[\begin{array}{ccc}2s&4\\2&s\end{array}\right] \left[\begin{array}{ccc}x_{1} \\x_{2} \end{array}\right] = \left[\begin{array}{ccc}-3 \\6 \end{array}\right]$

For the system to have a unique solution, $\begin{vmatrix} 2s & 4 \\ 2 & s \end{vmatrix} \neq 0$

$2s^{2} -8 \neq 0\\2s^{2}\neq 8\\s^{2}\neq 4\\s \neq 2 or -2$