The first equation has a coefficient of 1 on the y, so we'll solve the first equation for y to get
In the "other" equation, perform substitution to get rid of the variable we solved for in (1).
We substitute for y in the equation
2y + 6x = -8
After substituting, solve the "other" equation.
We simplify to get
-6x -8 + 6x = -8
Combining the x terms, we get
-8 = -8. We know this statement is true, because we just lost $8 the other day, and now we're $8 poorer. We left the money in our pants and sent them through the washer. We won't make that mistake again.
Since we've arrived at a statement that's always true, these two lines are really the same line, and every point on the line is a solution.