Answer:
See below
Step-by-step explanation:
Step 1. Write each inequality in the form y = x + b
(1) x + y > 2
(2) 2x – y > 1
(3) y > 2 - x Subtracted x from each side of (1)
-y > 1 – 2x Subtracted 2x from each side of 2
(4) y < 2x – 1 Multiplied each side by -1 and reversed the inequality
Step 2. Graph the functions as equalities
(5) y = 2 – x
(6) y = 2x - 1
The lines will form the boundaries of the inequalities. The condition will be true on one side of a line but not on the other (see the diagram below).
Step 3. Shade the areas of the graphs where the inequalities are true
The red line is the graph of y > 2 – x.
Since y is greater than a value on the high side of the line, shade the region above the line (red).
The blue line is the graph of y < 2x - 1.
Since y is less than a value on the low side of the line, shade the region below the line (blue).
The solution set for both inequalities is any point where the shaded regions overlap (purple).
Step 4. Verify the result.
Plug in a point in the shaded area, like (2, 2) and verify that each inequality holds.
(1) x + y > 2 (2) 2x – y >1
2 + 2 > 2 2(2) – 2 > 1
4 > 2 4 – 2 > 1
2 > 1
It checks.
The solution to the system of inequalities is
y > 2 – x, y < -1 + 2x
