Graph the system of inequalities
x¡Ü2
y¡Ý-2x+4
I am having trouble understanding what points to plot on the graph and also how the graph should be shaded (if at all).
I am not familiar with this notation at least the way it is coming up on my screen.
You probably mean < or > or ≥
If you can't generate these symbols, then use "words" to describe your relation
BTW, to get ≥ I hold down the Alt key while at the same time hitting 242 on the number pad of my PC running Windown XP
you can experiment with that starting with
Alt 1 to get ☺
sorry, it didn't post correctly.
Graph the system of inequalities
x (lesser or equal to sign)2
y (greater or equal to sign)-2x+4
I am having trouble understanding what points to plot on the graph and also how the graph should be shaded (if at all).
Well, first see what happens when x = 2
then y ≥ -4+4 so y ≥ 0
so the point (2,0) is at your upper x point and all y above that
Now what happens for a smaller x, such as x = 0?
if x = 0 then y≥4
so the point (0,4) is included and everything above that point.
Now I am going to go out on a limb and say everything above the line y=-2x+4 and to the left of the vertical line x = 2 is in your territory including the lines at the edges
To graph the system of inequalities x ≤ 2 and y ≥ -2x + 4, we will first graph each inequality separately and then identify the overlapping region.
Let's start with the first inequality, x ≤ 2:
Step 1: Draw a vertical line at x = 2. This line will act as a boundary for all the points that satisfy x ≤ 2.
Step 2: Since the inequality is "x ≤ 2," we need to shade the region to the left of the vertical line. The shading should include all points where x is less than or equal to 2.
Now let's move on to the second inequality, y ≥ -2x + 4:
Step 1: Begin by graphing the line y = -2x + 4. This line will act as a boundary for all the points that satisfy y ≥ -2x + 4.
Step 2: Since the inequality is "y ≥ -2x + 4," we need to shade the region above the line. The shading should include all points where y is greater than or equal to -2x + 4.
Finally, we will identify the overlapping region that satisfies both inequalities.
Step 1: Look for the region on the graph where the shading for both inequalities overlaps. This region represents the solution to both x ≤ 2 and y ≥ -2x + 4.
Step 2: Shade the overlapping region to make it stand out. This shaded region represents the solution to the system of inequalities.
In summary, when graphing the system of inequalities x ≤ 2 and y ≥ -2x + 4, you would plot the lines x = 2 and y = -2x + 4, shade the appropriate regions, and then identify the overlapping region as the solution.