The graphs are planes in 3 space, and their intersection is a line.
To plot a plane, you need 3 points.
Easiest 3 points to find are on the axes (e.g. x1 when x2 = x3 =0, x2 when x1=x3=0, ...)
Connect the 3 points and you will have triangle in the plane you want to sketch.
Your solution can be given as a parameteric line (let x2 on the right hand side be t)
x1 = t + 12
x2 = t
x3 = 5
Since x3 is constant, the line is parallel to the x1-x2 plane.
You already have it in the answer. The starting point is (12,0,5) and the direction vector is (1,1,0)