Graph the system of inequalities and determine if the point (10,2) is a solution. y≥−12x+6 y<4 Enter 1 for YES Enter 2 for NO (1 point)

Answer 1

To analyze the system of inequalities and determine if the point (10, 2) is a solution, let's first graph each inequality:

1. For the inequality \( y \geq -12x + 6 \):

   • The line \( y = -12x + 6 \) is the boundary line.
   • This line has a y-intercept at (0, 6) and a slope of -12.
   • To graph it, plot the y-intercept and use the slope to find another point. For example, from (0, 6), moving right 1 unit (to \(x = 1\)), move down 12 units to get to (1, -6).
   • Since it’s a "greater than or equal to" inequality, shade the region above the line.

2. For the inequality \( y < 4 \):

   • The line \( y = 4 \) is a horizontal line.
   • Since it’s a "less than" inequality, shade the region below this line.

Checking if the point (10, 2) satisfies both inequalities:

1. For \( y \geq -12x + 6 \):

   • Substitute \( x = 10\) and \( y = 2 \): \[ 2 \geq -12(10) + 6 \implies 2 \geq -120 + 6 \implies 2 \geq -114 \quad (\text{True}) \]

2. For \( y < 4 \):

   • Check the point \( (10, 2) \) for this inequality: \[ 2 < 4 \quad (\text{True}) \]

Since (10, 2) satisfies both inequalities, we conclude that it is indeed a solution.

Final Answer: 1 (YES)