Given the following system of equations:
[tex]\begin{cases}y=\frac{1}{2}x+4 \\ -x+2y=8\end{cases}[/tex]notice that we can use the first equation and substitute it on the second equation to get the following:
[tex]-x+2(\frac{1}{2}x+4)=8[/tex]then, solving for 'x', we get:
[tex]\begin{gathered} -x+2(\frac{1}{2}x+4)=8 \\ \Rightarrow-x+x+8=8 \\ \Rightarrow8=8 \end{gathered}[/tex]since the variable x was eliminated in the process of solving for it, we have that both equations represent the same line, therefore, there are infinite solutions for the system
