Recall that the slope-intercept form of the equations of a line is:
[tex]y=mx+b\text{.}[/tex]
Taking both equations to their slope-intercept form we get:
[tex]\begin{gathered} 6x+6y-6x=-30-6x, \\ 6y=-30-6x, \\ \frac{6y}{6}=-\frac{30}{6}-\frac{6}{6}x, \\ y=-x-5\text{.} \end{gathered}[/tex][tex]\begin{gathered} 3x+3y-3x=-15-3x, \\ 3y=-15-3x, \\ \frac{3y}{3}=-\frac{15}{3}-\frac{3}{3}x, \\ y=-x-5. \end{gathered}[/tex]
Notice that both equations are the same, therefore the system has infinitely many solutions, therefore it is consistent and dependent.
Answer:
Equations:
[tex]\begin{gathered} y=(-1)x+(-5), \\ y=(-1)x+(-5)\text{.} \end{gathered}[/tex]
The system is consistent and dependent.
A solution to the system is (0,-5).
