How do you graph the system #y >= - 2x - 3# and #3x - y > 2#?
1 Answer
A graph of a particular equation or inequality that involves two unknown variables
A graph of a system of equations or inequalities that involve two unknown variables
The above definition means that the graph of a system of equations or inequalities is an intersection of graphs representing each one of these equations or inequalities.
Draw a graph of the first inequality
graph{y>= -2x-3 [-10, 10, -5, 5]}
Draw a graph of the second inequality
graph{y < 3x-2 [-10, 10, -5, 5]}
All we need to do now is to intersect these two areas, and that would be a graph of a system of two inequalities.
To be precise, let's find the point of intersection of the left boundaries of both graphs (there is no right boundaries, the corresponding areas of the graphs infinitely continue as an argument
The point of intersection is, obviously, a solution of a system of equations:
To solve it, let's summarize left and right parts of both equations and get an equation for
Substituting this into the first equation gives
Therefore, the left boundary of the intersection of two areas represented by two graphs above has a key point
from which two lines are going - up along the line
The area of intersection would approximately look like this (except the lower part should be solid line which implies that the border is included):
graph{x+1/5>|y+13/5|/2 [-10, 10, -5, 5]}