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Is (1, 3) a solution to this system of inequalities?

y ≤ x + 2
y ≤ 3

1 answer

To determine if the point (1, 3) is a solution to the system of inequalities given by:

  1. \( y \leq x + 2 \)
  2. \( y \leq 3 \)

we need to substitute \( x = 1 \) and \( y = 3 \) into each inequality.

First inequality: \[ y \leq x + 2 \] Substituting the values: \[ 3 \leq 1 + 2 \] \[ 3 \leq 3 \] This is true.

Second inequality: \[ y \leq 3 \] Substituting the values: \[ 3 \leq 3 \] This is also true.

Since both inequalities are satisfied, the point (1, 3) is indeed a solution to the system of inequalities.