To graph a line, find two points that belong to that line, plot them into the coordinate plane and draw a line through them.
For instance, we can use x=0 to determine the corresponding value of y and then use y=0 to find the corresponding value of x, to plot the points.
For the first equation:
[tex]\begin{gathered} y=2x-1 \\ x=0\Rightarrow y=-1 \\ y=0\Rightarrow2x=1\Rightarrow x=\frac{1}{2} \end{gathered}[/tex]
Then, the following points belong to the first line:
[tex]\begin{gathered} (0,-1) \\ (\frac{1}{2},0) \end{gathered}[/tex]
Plot both boints on the coordinate plane and draw a line through them:
Use the same method to find two points over the second line.
[tex]\begin{gathered} -6x+3y=-3 \\ x=0\Rightarrow3y=-3\Rightarrow y=-1 \\ y=0\Rightarrow-6x=-3\Rightarrow x=\frac{1}{2} \end{gathered}[/tex]
Then, the following points belong to the line:
[tex]\begin{gathered} (0,-1) \\ (\frac{1}{2},0) \end{gathered}[/tex]
They turn out to be the same two points. Then, both lines overlap. Therefore, the system has infinite solutions.
