CUET UG 2025 — Mathematics Algebra

1. For the line $x - y = 5$x−y=5 (passes through $(5,0)$(5,0) and $(0,-5)$(0,−5)):

   • Inequality: $x - y \ge 5$x−y≥5
   • Testing $(0,0)$(0,0): $0 - 0 \ge 5 \implies 0 \ge 5$0−0≥5⟹0≥5 (False).
   • This means the region must be on the side away from the origin. Looking at the line passing through $(5,0)$(5,0), the origin is to its upper-left. So "away from the origin" means shading downward/lower-right.

2. For the line $5x - 5y = 16$5x−5y=16 (passes through $(16/5, 0)$(16/5,0) and $(0, -16/5)$(0,−16/5)):

   • Inequality: $5x - 5y \le 16$5x−5y≤16
   • Testing $(0,0)$(0,0): $0 - 0 \le 16 \implies 0 \le 16$0−0≤16⟹0≤16 (True).
   • This means the region must be on the side containing the origin. Looking at this upper line, the origin is to its upper-left. So "towards the origin" means shading upward/upper-left.

Conclusion:

• Graph 3 shades the region between the two lines.
• Graph 1 shades the regions running outwards: below the lower line ($x - y \ge 5$x−y≥5) and above the upper line ($5x - 5y \le 16$5x−5y≤16).