To determine if the point (1, 6) is a solution to the system of inequalities, we will substitute \( x = 1 \) and \( y = 6 \) into each inequality and check if it satisfies them.
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For the first inequality: \[ 2x + 3y ≥ 20 \] Substituting \( x = 1 \) and \( y = 6 \): \[ 2(1) + 3(6) ≥ 20 \] \[ 2 + 18 ≥ 20 \] \[ 20 ≥ 20 \] This inequality is satisfied.
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For the second inequality: \[ x + 2y < 13 \] Substituting \( x = 1 \) and \( y = 6 \): \[ 1 + 2(6) < 13 \] \[ 1 + 12 < 13 \] \[ 13 < 13 \] This inequality is not satisfied (it is false).
Since (1, 6) satisfies the first inequality but not the second, it is not a solution to the system of inequalities.