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Graph the solution X plus Y >4 and 2X minus Y less than or equal to three

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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.

Graph the solution X plus Y >4 and 2X minus Y less than or equal to three-example-1
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