The inequalities y < -x + 1 and y + 2 > x, plot the corresponding lines and shade the regions. The solution is the overlapping shaded area, satisfying both conditions.
The correct graph is graph 2.
To graph the solutions of the inequalities y < -x + 1 and y + 2 > x, we'll first graph the corresponding equations and then shade the regions determined by the inequalities.
Graph of y = -x + 1:
Start by plotting the y-intercept at (0, 1).
Use the slope of -1 (since the coefficient of x is -1) to plot another point, such as (1, 0).
Draw a line through these points.
Graph of y = -x + 2:
Start by plotting the y-intercept at (0, 2).
Use the slope of -1 to plot another point, such as (1, 1).
Draw a line through these points.
Shading for y < -x + 1:
Since y < -x + 1, shade the region below the line y = -x + 1. This is the region where y is less than the value determined by the line.
Shading for y + 2 > x:
Since y + 2 > x, rearrange it as y > x - 2 and shade the region above the line y = x - 2. This is the region where y is greater than the value determined by the line.
The solution to the system of inequalities is the overlapping shaded region, which satisfies both conditions.
Graph 2 is going to the correct option.