# Thread: Coordinates, vertices, and system of inequalities

1. ## Coordinates, vertices, and system of inequalities

find the coordinates of the vertices of the figure formed by the system of inequalities:
x ≥ -1, y ≥ -2, and 2x + y ≤ 6

having a hard time with this question,
step by step answers would help me out a lot, thanks in advanced.

2. ## Re: Coordinates, vertices, and system of inequalities

Originally Posted by jenbones
find the coordinates of the vertices of the figure formed by the system of inequalities:
x ≥ -1, y ≥ -2, and 2x + y ≤ 6

having a hard time with this question,
step by step answers would help me out a lot, thanks in advanced.
Just graph all three and look at it.

3. ## Re: Coordinates, vertices, and system of inequalities

You will need a graphing calculator with the app "inequalz" so that you can graph an X, or yu can graph by hand. First solve for Y for the third one so that you can put it in the calculator so y≤ 6-2x , x ≥ -1, y ≥ -2. Now enter in the calculator and then you will see the lines and the shaded region, (if not, then press zoom 6 which centers it or zoom in/out if needed.) now to see where all 3 shadings meet up, press alpha then y= then press 1 whcih i believe says inequal shade or whatever, and it will regrpah it with the shaded region of all the lines. to find the vertices of the feasible region (the shaded region) press alpha zoom which activates POI whcih measn point of intersection and that will find where all lines intersect. just move the arrows around to find vertices. (ability to graph X, alpha y= 1, and POI all come witht the app "inequalz" which can only be downloaded if you have a TI-83+ or more advanced version.)

By hand now is not that hard. anything y= or y ≤ or any inequality will be horizontal lines to y=1 will be a horizontal line 1 up from the origin. Anything x= or inequality will be vertical lines so x=1 will be a vertical line 1 right from the origin. so make your graph and if its ≤ or ≥ then its a solid line ( it no equal, then its dashed line)shaded under(less then or less than/equal to) or above (greater than or greater then/equal to) the line. for y≤ -2x+6 wil be started by going up six from the origin since it is a y inequality. put a point on (0,6) then you see the slope -2/1x means down 2, right 1 or up 2 and left 1 from the original point (0,6) so eac time you go down 2, right 1 plot a point and every time you go up 2 and left 1 plot a point. now once your done connect the dots for that equation and shade under it. it might look like a mess but if you can find the shaded region where all shades intersect, leave that region shaded only, which means all points in the shaded region or on the solid line bordering the shaded region could be plugged in to the 3 inequalities and work for all of them. I HOPE THIS HELPS!

4. ## Re: Coordinates, vertices, and system of inequalities

*so y=1 will be a horizontal line...
*(if no equal in the inequality, then its a dashed line)
[keep in mind that in equations/inequalities, start with K (the number that is added to the slope) then finally do the slope
*each time you go down two...
*dont connect all the dots, its should be a straight line of dots so draw a straigh line through the dots.
*= mispelling errors... haha