When graphing two-variable compound inequalities with "and", the shaded region is

When graphing two-variable compound inequalities with "and", the shaded region is

• A. The intersection of the half-planes
• B. The union of the half-planes
• C. The entire plane
• D. Only the boundary lines

Answer: (A)

When graphing two-variable inequalities with 'and', you want points that satisfy both inequalities at the same time. Each inequality creates a half-plane on one side of its boundary line. The shaded region for the first and the shaded region for the second overlap in the area where both conditions hold. That overlap is the intersection of the two half-planes. The boundary lines are included if the inequalities are inclusive (≤ or ≥); if they’re strict (< or >), the boundary lines aren’t included. This is different from using 'or', which would shade the union of the two half-planes.

When graphing two-variable inequalities with 'and', you want points that satisfy both inequalities at the same time. Each inequality creates a half-plane on one side of its boundary line. The shaded region for the first and the shaded region for the second overlap in the area where both conditions hold. That overlap is the intersection of the two half-planes. The boundary lines are included if the inequalities are inclusive (≤ or ≥); if they’re strict (< or >), the boundary lines aren’t included. This is different from using 'or', which would shade the union of the two half-planes.