If the system of linear equations 2x + y = 1 and y = − 12 x + 1 are graphed on the same coordinate grid, which of the following is the solut

Well, first of all I don't see "the following" solutions, but no worries!

You can graph the two equations in a graphing calculator by writing them in the y = mx + b form, where m is slope and b is the y-intercept.

For the first equation 2x + y = 1 you would move the 2x to the right and rewrite it as:

y = -2x + 1

The second equation stays the way it is: 

y = -12x + 1

Now graph both of them on the same axes, and look at the point where they intersect.

They intersect at (0, 1)

The easiest way to solve is to see that y=1-2x=1-12x or -2x=-12x or -10x=0 so x=0.

Notice that each line has a different slope but both have the same y intercept. So their point of intersection = (0,1).