I need some help with solving this problem:
Find the solution set for the system of linear inequalities.
x – y ≥ 3
x + 2y ≥ 6
Please use the same name for your posts.
To find the solution set for this system of linear inequalities, you can follow these steps:
Step 1: Graph each inequality separately.
Start by graphing each inequality on the coordinate plane. Since these are linear inequalities, you can use either the slope-intercept form or the intercept method to graph them.
For the first inequality, x - y ≥ 3:
a) Rewrite it in slope-intercept form: y ≤ x - 3
b) To graph it, start with the line y = x - 3. Since it is a "less than or equal to" inequality, the line should be a solid line.
c) Shade the region below the line to indicate all the solutions that satisfy this inequality.
For the second inequality, x + 2y ≥ 6:
a) Rewrite it in slope-intercept form: y ≥ -(1/2)x + 3
b) To graph it, start with the line y = -(1/2)x + 3. Since it is a "greater than or equal to" inequality, the line should be a solid line.
c) Shade the region above the line to indicate all the solutions that satisfy this inequality.
Step 2: Determine the overlapping region.
The overlapping region where the shaded regions of both inequalities intersect represents the solution set for the system of linear inequalities.
Step 3: Identify the solution set.
Look at the overlapping region and identify the points within that region. These points satisfy both inequalities and form the solution set.
That's it! By following these steps, you can find the solution set for the given system of linear inequalities.