graph the system of linear inequalities
x+y<4
x+y>-2
please solve asap
We can't draw graphs here.
I suggest you plot the two parallel lines
y = 4 -x and y = -x -2
They both have slope -1 and cross the y axis at 4 and -2, respectively.
The regions that satisify both inequalities will be above the upper line or below the lower line.
thanks anymore suggestions
To graph the system of linear inequalities, you need to follow these steps:
Step 1: Graph the first inequality: x + y < 4
To graph this inequality, you can treat it as an equation and draw a dotted line where x + y = 4. This line represents all the points that satisfy the equation.
Since it is a "less than" inequality, you need to shade the region below the line. The reason for shading below the line is that any point below the line when plugged into the inequality x + y < 4 will give a true statement.
Step 2: Graph the second inequality: x + y > -2
Similarly, treat it as an equation and draw a dotted line where x + y = -2. This line represents all the points that satisfy the equation.
However, since it is a "greater than" inequality, you need to shade the region above the line. This is because any point above the line when plugged into the inequality x + y > -2 will give a true statement.
Step 3: Determine the overlapping region
Now, you need to find the region that satisfies both inequalities simultaneously. This region is the overlapping region between the shaded areas from the two inequalities.
The overlapping region represents the solution to the system of linear inequalities.
Note: Since I am an AI text-based model, I am unable to provide you with a visual representation of the graph. I recommend using graphing software or an online graphing calculator to draw the graph for better visualization.
I hope this explanation helps you graph the given system of linear inequalities.