Answer:
The lines are parallel
Explanation:
Given the equations;
[tex]\begin{gathered} y=2x+6------1 \\ 3y=6x-6------2 \end{gathered}[/tex]
To simplify equation 2, let us divide equation 2 through by 3;
[tex]\begin{gathered} \frac{3y}{3}=\frac{6x}{3}-\frac{6}{3} \\ y=2x-2-------------2a \end{gathered}[/tex]
Comparing equation 1 to equation 2a;
[tex]\begin{gathered} y=2x+6-------1 \\ y=2x-2-------2a \end{gathered}[/tex]
The slope of the equations are;
[tex]\begin{gathered} y=mx+b \\ m_1=2 \\ m_{2a}=2 \end{gathered}[/tex]
Since the slope of the two equations are both equal to 2 ( equal), then the lines of the equations will be parallel.
Therefore, The lines are parallel
