To determine if the point (3, -9) is a solution to the system of inequalities, we will substitute \( x = 3 \) and \( y = -9 \) into each inequality and check if they hold true.
-
First inequality: \[ 7x + 20y < -13 \] Substitute \( x = 3 \) and \( y = -9 \): \[ 7(3) + 20(-9) < -13 \] \[ 21 - 180 < -13 \] \[ -159 < -13 \] This inequality is true.
-
Second inequality: \[ 18x - 7y > -10 \] Substitute \( x = 3 \) and \( y = -9 \): \[ 18(3) - 7(-9) > -10 \] \[ 54 + 63 > -10 \] \[ 117 > -10 \] This inequality is also true.
Since both inequalities are satisfied by the point (3, -9), we conclude that (3, -9) is indeed a solution to the system of inequalities.