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.
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Option #1: (212,−12)
Substitute \( x = 212 \) and \( y = -12 \):
\( 4(212) - (-12) \leq 10 \)
\( 848 + 12 \leq 10 \)
\( 860 \leq 10 \) (False) -
Option #2: (2,−3)
Substitute \( x = 2 \) and \( y = -3 \):
\( 4(2) - (-3) \leq 10 \)
\( 8 + 3 \leq 10 \)
\( 11 \leq 10 \) (False) -
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 \( 4x - y \leq 10 \).