Question

I need help solving this problem. i have been stuck on it for hours. please help

Answer 1

So, the idea behind the elimination is that, you multiply either or both equations by some factor, so that one variable, get a negative twin, and then the twins cancel each other... so... let's do so by multiplying the bottom equation by 3, so we end up with "3d" at the bottom and -3d + 3d zaps each other.

$\bf \begin{array}{lllllll} 9a-3d=3&&~~~9a\underline{-3d}=3\\ -3a+d=-1\implies &\boxed{\times 3}\implies &-9a\underline{+3d}=-3\\ &&--------\\ &&~~0~+~~0 = 0 \end{array}$

holy macaroni, all the values went kaput.... so, what's cooking?

well, it turns out that, the top equation is really the bottom equation in disguise, so both equations are really twins, and therefore they have infinitely many solutions, not just one solution.

graph wise, if you graph one and graph the other, what will occur is that, one will be pancaked on top of the other, and so every single point in the graph is solution.