Question

How many solutions does the following system have and what is the solution to the system if any

Answer 1

First, we multiply the first equation by 2.

`\begin{gathered} (2)(-5x-y)=(2)\cdot4 \\ -10x-2y=8 \end{gathered}`

Then, we sum this equation with the second one in the given system.

`\begin{gathered} \mleft\{\begin{aligned}-10x-2y=8 \\ 10x+2y=8\end{aligned}\mright. \\ 10x-10x+2y-2y=8+8 \\ 0x+0y=16 \\ 0=16 \end{gathered}`

As you can observe, we've got a false result because zero is not equal to 16.

Therefore, the system has no solutions at all.