Answer :
Given the system of equations:
[tex]\begin{gathered} 3x+y=2 \\ 6x+2y=4 \end{gathered}[/tex]We will use the elimination method to solve the system of equations:
So, we will multiply the first equation by (-2) to eliminate y:
[tex]\begin{gathered} 3x+y=2\rightarrow(\times-2) \\ 6x+2y=4 \\ ========= \\ -6x-2y=-4 \\ 6x+2y=4 \end{gathered}[/tex]Add the equations:
[tex]\begin{gathered} (-6x+6x)+(-2y+2y)=-4+4 \\ 0=0 \end{gathered}[/tex]The last result means that the system is consistent dependent
So, there are the infinite solutions because the equations represent the same line
So, the answer will be an infinite solution