Graph the solution set for the of linear inequalities.
x−y≤3
x+3y≤3
x≥−2
I answered the almost identical question for you this noon.
Follow the same steps
https://www.jiskha.com/questions/1775840/Graph-the-solution-set-for-the-of-linear-inequalities-x-y-4-x-3y-4-x-5
To graph the solution set for the system of linear inequalities, we will start by graphing each inequality separately and then determine the overlapping region.
1. Graph the first inequality: x - y ≤ 3
To graph this inequality, we can start by converting it into slope-intercept form. Rearranging the equation, we have:
y ≥ x - 3
To graph this, we can plot the line y = x - 3 as a dashed line. Since we have a "greater than or equal to" sign, we will make the line solid.
Next, since we want to shade the region where y is greater than or equal to x - 3, we can shade the area above the line.
2. Graph the second inequality: x + 3y ≤ 3
Similarly, we rearrange the inequality into slope-intercept form:
y ≤ (3 - x)/3
Plot the line y = (3 - x)/3 as a dashed line. Since we have a "less than or equal to" sign, the line will be solid. Shade the region below the line, as we want y to be less than or equal to (3 - x)/3.
3. Graph the third inequality: x ≥ -2
For this inequality, we have a "greater than or equal to" sign, so the line will be solid. Plot the vertical line x = -2, and shade the region to the right of the line, as we want x to be greater than or equal to -2.
Now, we can observe the overlapping region of all the shaded areas from the three inequalities. The overlapping region represents the solution set for the system of linear inequalities.
Please note that without specific coordinates, it is difficult to provide an accurate graphical representation. It is recommended to use a graphing tool or graph paper to accurately plot the lines and shade the regions.
To graph the solution set for a system of linear inequalities, we will start by graphing each inequality individually and shade the regions that satisfy the inequality.
1. Let's start with the first inequality: x - y ≤ 3.
Step 1: Rewrite the inequality in slope-intercept form to graph it more easily.
x - y ≤ 3
-y ≤ -x + 3
y ≥ x - 3 (multiply by -1 and flip the inequality sign)
Step 2: Start by graphing the equality y = x - 3. This line has a slope of 1 and y-intercept of -3. Draw this line with a dashed line.
Step 3: Choose a test point not on the line. For simplicity, we can use the origin (0,0).
Substitute the x and y-coordinates of the test point into the inequality:
0 ≥ 0 - 3
0 ≥ -3
Since the inequality is true, shade the region above the line.
2. Moving on to the second inequality: x + 3y ≤ 3.
Step 1: Rewrite the inequality in slope-intercept form.
x + 3y ≤ 3
Step 2: Graph the equality line x + 3y = 3. Rearrange the equation to solve for y:
3y ≤ -x + 3
y ≤ (-1/3)x + 1 (divide both sides by 3)
The line has a slope of -1/3 and y-intercept of 1. Draw this line with a dashed line.
Step 3: Choose a test point not on the line. Again, we can use the origin (0,0).
Substitute the x and y-coordinates of the test point into the inequality:
0 ≤ 0 + 3*0
0 ≤ 0
Since the inequality is true, shade the region below the line.
3. Finally, let's graph the third inequality: x ≥ -2.
This inequality represents a vertical line passing through x = -2. Since it is an inequality with a "greater than or equal to" sign, we will draw a solid line.
Shade the region to the right of the line.
Step 4: Identify the overlapping region shaded by all three inequalities. This overlapping region represents the solution set for the system of linear inequalities.
Now, plot the shaded regions for each inequality on the same graph. The overlapping shaded region is the solution set for the system of linear inequalities.