Question

1. Solve the following system using the substitution, elimination, or graphing method for the y coordinate.

Answer 1

Note that the 2nd equation can be re-written as x+4y=3, or x = -4x + 3, which is exactly the same thing as the 1st equation.  

Thus, there are infinitely many solutions to this system.

Answer 2

$\bf \begin{cases} \boxed{x}=-4y+3\\ -x-4y=-3\\ -----------\\ -\left( \boxed{-4y+3} \right)-4y=-3 \end{cases} \\\\\\ 4y-3-4y=-3\implies \stackrel{\textit{another way of saying the equations are identical}}{0=0}$

so the 2nd equation is really the first equation in disguise.

since both equations are the same, that means if you graph them, is just one line pancaked over the other, and the solutions points is every single one on each, namely infinitely many solutions.