Question

give the solution of the system. if the system has no solution or an infinite number of solutions, say so. if the system has one solution, find it.\\\

$$\begin{cases}2x - y = 17\\\\-8x + 4y = 0\\end{cases}$$

\when solving, you obtain $0 = 68$.\
select the correct choice below and, if necessary, fill in the answer box to complete your choice.\
\\(\bigcirc\\) a. the solution is \\(\square\\).\
\\(\quad\\) (simplify your answer. type an ordered pair.)\
\\(\bigcirc\\) b. there is an infinite number of solutions.\
\\(\bigcirc\\) c. there is no solution.

Explanation:

To solve a system of linear equations, we can use methods like elimination or substitution. In this case, when solving the system \(

$$\begin{cases}2x - y = 17\\-8x + 4y = 0\end{cases}$$

\), we end up with a contradiction \(0 = 68\). A contradiction means that there are no values of \(x\) and \(y\) that can satisfy both equations simultaneously. So the system has no solution.

Answer:

C. There is no solution.