Graph x+y<=2 and x>=1

Problem

x+y≤2,x≥1

Solution

1. Identify the boundary lines for the inequalities by replacing the inequality signs with equals signs, resulting in x+y=2 and x=1

2. Graph the first boundary line x+y=2 by finding its intercepts: when x=0 y=2 and when y=0 x=2 Draw a solid line through (0,2) and (2,0) because the inequality is ≤

3. Determine the shaded region for x+y≤2 by testing a point like (0,0) Since 0+0≤2 is true, shade the region below and to the left of the line.

4. Graph the second boundary line x=1 which is a solid vertical line passing through x=1 on the x-axis.

5. Determine the shaded region for x≥1 by shading everything to the right of the vertical line x=1

6. Find the intersection of the two shaded regions. The solution is the triangular area bounded by the lines x=1 x+y=2 and extending downwards where both conditions are met.

Final Answer

x+y≤2∩x≥1

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