Which of the following points is a solution to the linear inequality 4x−y≤10 , as shown on the graph? Option #1: (212,−12) Option #2: (2,−3) Option #3: (3,2) (1 point) The point in Option # is a solution to the linear inequality 4x−y≤10 .

Answer 1

To determine which point is a solution to the linear inequality \( 4x - y \leq 10 \), we can test each option by substituting the values of \( x \) and \( y \) into the inequality.

1. Option #1: (212,−12)
   Substitute \( x = 212 \) and \( y = -12 \):
   \( 4(212) - (-12) \leq 10 \)
   \( 848 + 12 \leq 10 \)
   \( 860 \leq 10 \) (False)

2. Option #2: (2,−3)
   Substitute \( x = 2 \) and \( y = -3 \):
   \( 4(2) - (-3) \leq 10 \)
   \( 8 + 3 \leq 10 \)
   \( 11 \leq 10 \) (False)

3. Option #3: (3,2)
   Substitute \( x = 3 \) and \( y = 2 \):
   \( 4(3) - 2 \leq 10 \)
   \( 12 - 2 \leq 10 \)
   \( 10 \leq 10 \) (True)

The point in Option #3, (3, 2), is a solution to the linear inequality \( 4x - y \leq 10 \).