Graph the system: Shade above X+Y=4 and below 2X−Y≤3. Overlapping region is the solution.
To graph the system of inequalities X+Y>4 and 2X−Y≤3, we can start by graphing each inequality separately and then finding the overlapping region.
Let's start with the first inequality
X+Y>4:
Graph the line X+Y=4. This line is represented by the equation
X+Y=4, and it separates the plane into two regions.
To graph this line, we can rewrite it in slope-intercept form (Y=mx+b):
Y=−X+4
The slope (m) is -1, and the y-intercept (b) is 4.
Since the inequality is X+Y>4, we want to shade the region above the line because any point in that region satisfies the inequality.
Now, let's move on to the second inequality 2X−Y≤3:
Graph the line 2X−Y=3. This line is represented by the equation
2X−Y=3, and it also separates the plane into two regions.
To graph this line, we can rewrite it in slope-intercept form:
Y=2X−3
The slope (m) is 2, and the y-intercept (b) is -3.
Since the inequality is 2X−Y≤3, we want to shade the region below the line, including the line itself.