Answer
The system of linear equations has infinitely many solutions and the solution set is\[\left\{ \left( x,y \right)|4x-2y=2 \right\}\].
Work Step by Step
The system of linear equation:
\[\begin{align}
& 4x-2y=2 \\
& 2x-y=1
\end{align}\]
Multiply \[2\]on both sides to the equation\[2x-y=1\], and get: \[4x-2y=2\].
Subtract the second given equation to the above obtained equation from both RHS and LHS as follows:
\[\underline{\begin{align}
& 4x-2y=2 \\
& -4x+2y=-2
\end{align}}\]
\[\ \ \ \ \ \ \ \ \ \ \ 0=0\]
Since,\[0=0\] it implies that the system of linear equations has infinitely many solutions.
The two lines coincide and all the points lying on the lines are the solution to the system of the linear equations.
Therefore the solution set is\[\left\{ \left( x,y \right)|4x-2y=2 \right\}\].
Hence, the system of linear equations has infinitely many solutions and the solution set is
\[\left\{ \left( x,y \right)|4x-2y=2 \right\}\].
