To determine if the point (1, 3) is a solution to the system of inequalities, we need to substitute \( x = 1 \) and \( y = 3 \) into each inequality and see if they hold true.
-
For the first inequality: \( 2x + y < 6 \)
Substitute \( x = 1 \) and \( y = 3 \): \[ 2(1) + 3 < 6 \ 2 + 3 < 6 \ 5 < 6 \] This inequality is true.
-
For the second inequality: \( 10x + 2y \geq 20 \)
Substitute \( x = 1 \) and \( y = 3 \): \[ 10(1) + 2(3) \geq 20 \ 10 + 6 \geq 20 \ 16 \geq 20 \] This inequality is false.
Since the point (1, 3) satisfies the first inequality but fails the second, it is not a solution to the system of inequalities.