The Solution:
Given the system of equations below:
[tex]\begin{gathered} y=-4x-2 \\ y=-4x+7 \end{gathered}[/tex]
We are required to determine the number of solutions for the given linear system.
Parallel Lines: If the two linear equations have the same slope (and different y-intercepts), the lines will be parallel. Since parallel lines never intersect, a system made up of two parallel lines will have NO solution since there is no intersection of the lines.
Equating both equations, we have:
[tex]\begin{gathered} -4x-2=-4x+7 \\ \text{Collecting the like terms, we get} \end{gathered}[/tex][tex]\begin{gathered} -4x+4x=7+2 \\ 0=9 \end{gathered}[/tex]
This means that there is NO SOLUTION for the two equations.
