SOLUTION: 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 + 4

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.

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