Solve the system of two linear inequalities graphically. y≤−5x+10 y>x−2 Find the region with points that satisfy both inequalities. Select the region you wish to be shaded A, B, C or D
To solve the system of linear inequalities graphically, we need to find the region where both inequalities are satisfied.
First, let's graph the first inequality y ≤ -5x + 10:
To graph this inequality, we can start by graphing the line y = -5x + 10. This line has a y-intercept of (0, 10) and a slope of -5. We can plot these two points and draw a straight line through them.
Next, we need to determine which side of the line to shade. Since the inequality is y ≤ -5x + 10, we need to shade the side of the line that is below the line itself.
Now, let's graph the second inequality y > x - 2:
To graph this inequality, we can start by graphing the line y = x - 2. This line has a y-intercept of (0, -2) and a slope of 1. We can plot these two points and draw a straight line through them.
Next, we need to determine which side of the line to shade. Since the inequality is y > x - 2, we need to shade the side of the line that is above the line itself.
Finally, we can identify the region where both inequalities are satisfied by looking for the overlapping shaded regions.
The region where both inequalities are satisfied is region A, which is shaded.