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Is (–10, 2) a solution to this system of inequalities?

7x − 2y < –18
2x + 19y > 13

1 answer

To determine if the point \((-10, 2)\) is a solution to the system of inequalities, we will substitute \(x = -10\) and \(y = 2\) into each inequality.

  1. First inequality: \[ 7x - 2y < -18 \] Substituting the values: \[ 7(-10) - 2(2) < -18 \] \[ -70 - 4 < -18 \] \[ -74 < -18 \] This is false.

  2. Second inequality: \[ 2x + 19y > 13 \] Substituting the values: \[ 2(-10) + 19(2) > 13 \] \[ -20 + 38 > 13 \] \[ 18 > 13 \] This is true.

Since \((-10, 2)\) does not satisfy the first inequality, it is not a solution to the system of inequalities.