Answer
The system of linear equations has infinitely many solutions and the solution set is
\[\left\{ \left( x,y \right)|x+3y=2 \right\}\]or\[\left\{ \left( x,y \right)|3x+9y=6 \right\}\].
Work Step by Step
Multiply \[3\]on both sides of the equation \[x+3y=2\]to get \[3x+9y=6\].
Subtract the second given equation from the above obtained equation on both RHS and LHS as follows:
\[\underline{\begin{align}
& 3x+9y=6 \\
& -3x-9y=-6
\end{align}}\]
\[\ \ \ \ \ \ \ \ \ \ 0=0\]
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
\[\left\{ \left( x,y \right)|x+3y=2 \right\}\]or\[\left\{ \left( x,y \right)|3x+9y=6 \right\}\].
