Answer:
Inconsistent: parallel lines.
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y=4x+4\\-12x+3y=3\end{cases}[/tex]
Use arithmetic operations to isolate y in the second equation:
[tex]\implies -12x+3y+12x=3+12x[/tex]
[tex]\implies 3y=12x+3[/tex]
[tex]\implies\dfrac{3y}{3}=\dfrac{12x}{3}+\dfrac{3}{3}[/tex]
[tex]\implies y=4x+1[/tex]
Therefore, we can see that both equations have the same slope and so the graphs of these equations are parallel.
The solution to a system of linear equations is the point of intersection.
As parallel lines never intersect, there are no solutions to this system and the system is said to be inconsistent.
