You can start with y = 3x-4 and subtract 3x from both sides to get
y = 3x-4
y-3x = 3x-4-3x
-3x+y = -4
So the first equation transforms into -3x+y = -4
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We have this system of equations
[tex]\begin{cases}-3x+y = -4\\-3x+y = 4\end{cases}[/tex]
The left hand side is the same expression. Let's make z = -3x+y
So our updated system is now
[tex]\begin{cases}z = -4\\z = 4\end{cases}[/tex]
but this is not possible to have a single variable equal to more than one number at a time. Either z is -4 or it is 4, but it cannot be both at the same time.
Therefore, this system is considered inconsistent and it has no solutions.
If you were to graph each equation (as shown below), you would have two parallel lines that never cross. An intersection point is a solution to a system. Having no intersection points means there are no solutions.
Answer: There are no points of intersection
