Suppose that y varies inversely with x. write an equation for the inverse variation y=4 when x=7

If y varies inversely as x, then we write it as:

y = k/x

where k is some constant.

If we multiply both sides of this equation by x we get an equation for k:

k = x*y

We are given that y=4 when x=7, therefore:

k = 7*4 = 28

Put this back into our original equation to get:

y = 28/x

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.