Brainliest given to correct answer consider the equation 2y – 4x = 12. which equation, when graphed with the given equation, will form a system with one solution?

The solution to a system of (linear) equations is the point where the graphs intersect. Consider two parallel lines. By definition, two parallel lines never intersect each other, but all pairs of non-parallel lines will eventually intersect. That means they will also have a solution.

Let's consider what makes a line parallel to another line. It basically looks identical, having the same steepness (slope), but the graph is just shifted over. That is, a parallel line would have the same slope and a different y-intercept. For our equation , or  in slope-intercept form, a parallel line will be of the form .

That describes the form of a parallel line, which we do not want. Any other line, however, will give a solution to our system, so we merely want a line where the slope does not equal 2.

We can have any equation of the form .