Graph the solution of the system of linear inequalities.
{y ≥ - x + 3
{y ≤ 2x + 5
To graph the solution of the system of linear inequalities, we first need to graph each inequality separately.
For the inequality y ≥ -x + 3, we start by graphing the line y = -x + 3. This line has a y-intercept of 3 and a slope of -1 (meaning for every unit increase in x, y decreases by 1).
Graphing the line y = -x + 3 gives us:
Now we need to determine which side of the line represents the solution to the inequality. Since y is greater than or equal to the line, we shade the region above the line.
Next, we graph the inequality y ≤ 2x + 5. We start by graphing the line y = 2x + 5. This line has a y-intercept of 5 and a slope of 2 (meaning for every unit increase in x, y increases by 2).
Graphing the line y = 2x + 5 gives us:
Again, we shade the region below the line since y is less than or equal to the line.
Now we look at the shaded regions for each inequality and find the region where they overlap. The overlapping region represents the solution to the system of linear inequalities.
Combining the shaded regions, we get:
Thus, the graph of the solution to the system of linear inequalities is the shaded region where the two overlapping regions meet.