How to find the points of a triangle in a Cartesian plane?

Question

In the Cartesian plane, a triangle formed by the three lines, r1: = 0, r2 = 2x, r3 = -x+7 

What are the points that lie inside the triangle?

Answer 1

Draw a figure.  You will have a triangle and one vertex is at (7/3,14/3) which you get by solving the system

y = 2x and

y = -x + 7

 

for 0<x≤7/3, y<2x describes the points

 

for 7/3<x<7, I will let you figure out how to describe the points using the above answer as a hint.