Solve the system of inequalities by graphing.
y ≤ 6
y ≤ -9x + 1
Select a line to change it between solid and dotted. Select a region to shade it.
Solve the system of inequalities by graphing. y ≤ 6 y ≤ -9x + 1 Select a line to change it between solid and dotted. Select a region to shade it.
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To solve the system of inequalities by graphing, let’s start with each inequality:
1. First inequality: ( y leq 6 )
– This represents a horizontal line at ( y = 6 ). Since the inequality is “less than or equal to,” you will draw a solid line. The region below this line will be shaded.
2. Second inequality: ( y leq -9x + 1 )
– To graph this line, first find the y-intercept, which is at ( (0, 1) ). The slope is -9, which means for every 1 unit you move to the right (positive x-direction), you move down 9 units (negative y-direction).
– This line should also be solid because of the “less than or equal to” sign. Shade the region below this line as well.
### Steps to graph:
– Draw a horizontal solid line at ( y = 6 ) and shade below it.
– Plot the y-intercept at ( (0, 1) ) and use the slope to find another point, such as ( (1, -8) ). Draw a solid line through these points and shade below this line.
### Conclusion:
The solution to the system of inequalities is the overlapping shaded region below both lines. This region represents all the points ( (x,y) ) that satisfy both inequalities.
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