Answer
Infinitely many solutions.
Work Step by Step
The given system of equations is
$x-2y=1$
$-2x+4y=-2$
The augmented matrix is
$\Rightarrow \left[\begin{array}{cc|c}
1 & -2 & 1\\
-2 & 4 & -2
\end{array}\right]$
Perform $R_2\rightarrow R_2+2\times R_1$.
$\Rightarrow \left[\begin{array}{cc|c}
1 & -2 & 1\\
-2+2\times 1 & 4+2\times (-2) & -2+2\times (1)
\end{array}\right]$
Simplify.
$\Rightarrow \left[\begin{array}{cc|c}
1 & -2 & 1\\
0 & 0 & 0
\end{array}\right]$
Use back substitution to solve the linear system.
$\Rightarrow (1)x+(-2)y=1$
and
$\Rightarrow (0)x+(0)y=0$
From the second equation we can say that the system has infinitely many solutions.
