Question 28678: 1. Solve the following system of linear inequalities by graphing.
x + 2y <= 3
2x – 3y <= 6
2. Solve the following system of linear inequalities by graphing.
3x + 4y <=12
x + 3y <= 6
x => 0
y => 0
Please help!
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! First, plot or sketch the first 2 straight lines:
 is the brown line, also quoted as 
 is the green line, also quoted as 
So, for the first equation... pick a point that is NOT on the line. And pick a nice easy point ie one with small numbers...i choose the origin (0,0).
y and (-3/4)x + 3
--> 0 and (-3/4)(0) + 3
--> 0 and 0 + 3
--> 0 and 3
--> zero is less than 3
so is the region below the line... SHADE EVERYTHING ABOVE THE LINE, as this is NOT wanted.
Repeat for the second line, and pick a point, again i pick (0,0):
y and (-1/3)x + 2
--> 0 and (-1/3)(0) + 2
--> 0 and 0+2
--> 0 and 2
--> zero is LESS than 2
so is the region below that line... SHADE EVERYTHING ABOVE THE LINE, as this is NOT wanted.
And now, the third line,  . Well x=0 is the y-axis. And we want every point/place on the graph that is greater or equal to that line...this is everything to the right of the y-axis. SHADE EVERYTHING TO THE LEFT OF THE y-axis, as this is NOT wanted.
And now, the last line,  . Well, y=0 is the x-axis. And we want every point/place on the graph that is greater or equal to that line... this is everything above the x-axis. SHADE EVERYTHING BELOW THE x-axis, as this is NOT wanted.
What region is left clear? is is the little 4-sided shape in the middle, bounded by the x- and y-axis and the 2 straight lines forming a ^ shape.
jon.
|
|
|
