Question

Y=-6x-4 12x+2y=-7 substitution

Answer 1

`\begin{cases} y=-6x-4\\\\ 12x+2y=-7 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{substituting} }{12x+2(-6x-4)=-7}\implies 12x-12x-8=-7\implies -8\\e -7`

what the heck happened!!!!

well, that's usually a flag to "no solution" sometimes you'd get stuff like 0 = 6 or -15 = 3 or so, which is just a flag for that, now, hmm let's put the 2nd equation in slope-intercept form

`\hspace{18.5em} y=\stackrel{ \stackrel{m}{\downarrow } }{-6} x-4 \\\\[-0.35em] ~\dotfill\\\\ 12x+2y=-7\implies 2y=-12x-7\implies y=\stackrel{ \stackrel{m}{\downarrow } }{-6} x-\cfrac{7}{2}`

notice, they have the same slope, but different y-intercept, the hell does that mean? well, it means both lines are parallel to each other and away by a few units, they never touch, since they never touch, no solutions ever.

Answer 2

12x + 2(-6x-4) = -7

12x + -12x -8 = -7

-8=-7

There is no solution