Graph the system of inequalities, and label each with a vertex with its coordinates.
y-2x≥-3
y+3>−x
3y−2x≤12
2y+x<8
I did graph this but I'm having a hard time to label each vertex with its coordinates.
hh? If you have the graphs, just mark where the lines intersect. I assume your graph looked kind of like this:
http://www.wolframalpha.com/input/?i=plot+y-2x%E2%89%A5-3,+y%2B3%3E%E2%88%92x,+3y%E2%88%922%E2%80%8Bx%E2%89%A412,+2y%2Bx%3C8
Now, the lowest vertex is the intersection of the lines
y-2x = -3
y+3 = -x
Pick other pairs of lines and you can find the other vertex coordinates.
Yes it did. However, the points I found don't match the answer when I plug x and y back in the equation
For ex. Point (0, 4) that works in the equation 3 and 4.
Point (-4.25,1.25) does not work in equation 2 and 3.
Point (0,-3) does not work in equation 1 and 2
Point (2.75,2.5) does not work on eqaution 1 and 4.
so, if those points do not work, why are you mentioning them? Surely you can find the intersections of two lines ... ?? Got some work to show?
There are 6 pairs of lines, but two of them intersect outside the shaded region.
To graph the system of inequalities and label each vertex with its coordinates, follow these steps:
Step 1: Graph each inequality individually:
- To graph the inequality y - 2x ≥ -3, start by graphing the equation y - 2x = -3 by first determining its slope-intercept form. Rearrange the equation to y = 2x - 3. Plot the y-intercept at (0, -3) and use the slope to plot more points. Since the inequality includes y ≥, the graph should be a solid line shaded above the line.
- Next, graph the inequality y + 3 > -x. Rewrite the inequality in slope-intercept form as y > -x - 3. Plot the y-intercept at (0, -3) and use the negative slope to plot additional points. Since the inequality indicates y >, the graph should be a dashed line shaded above the line.
- Similarly, graph the inequalities 3y - 2x ≤ 12 and 2y + x < 8. Convert each inequality to slope-intercept form, plot the lines, and shade the appropriate regions.
Step 2: Find the coordinates of each vertex:
- The vertices are the points where the boundary lines intersect. To find these points, solve the system of equations formed by the intersection of each pair of boundary lines.
Step 3: Label each vertex with its coordinates:
- Once you have the solution (x, y) for each intersection point, write the coordinates on the graph near the intersection.
Note: It's important to accurately interpret the inequalities and shade the appropriate regions (above or below the lines). The points where shaded regions overlap will form the feasible region for the system of inequalities, and these corresponding vertices will be labeled.
If you are still facing difficulties labeling the vertices, it could be helpful to provide the graph you have plotted, and I can guide you further in labeling the vertices with their correct coordinates.