Question

9.71.
multiple choice: which of the points below is a solution of ( y < |x - 3| )?
homework help
a. ( (2,1) )
b. ( (-4,5) )
c. ( (-2,8) )
d. ( (0,3) )
b. is ( (0,0) ) a solution to this system? how can you tell?

Explanation:

To determine which point is a solution to the inequality \( y < |x - 3| \), we substitute the \( x \)- and \( y \)-values of each point into the inequality and check if the inequality holds true.

Part a: Point \((2, 1)\)

• Substitute \( x = 2 \) and \( y = 1 \) into \( y < |x - 3| \):
• First, calculate \( |2 - 3| = |-1| = 1 \).
• Now, check if \( 1 < 1 \). Since \( 1 \) is not less than \( 1 \) (it is equal), the inequality does not hold. Thus, \((2, 1)\) is not a solution.

Part b: Point \((-4, 5)\)

• Substitute \( x = -4 \) and \( y = 5 \) into \( y < |x - 3| \):
• Calculate \( |-4 - 3| = |-7| = 7 \).
• Check if \( 5 < 7 \). Since \( 5 \) is less than \( 7 \), the inequality holds. Thus, \((-4, 5)\) is a solution.

Part c: Point \((-2, 8)\)

• Substitute \( x = -2 \) and \( y = 8 \) into \( y < |x - 3| \):
• Calculate \( |-2 - 3| = |-5| = 5 \).
• Check if \( 8 < 5 \). Since \( 8 \) is not less than \( 5 \), the inequality does not hold. Thus, \((-2, 8)\) is not a solution.

Part d: Point \((0, 3)\)

• Substitute \( x = 0 \) and \( y = 3 \) into \( y < |x - 3| \):
• Calculate \( |0 - 3| = |-3| = 3 \).
• Check if \( 3 < 3 \). Since \( 3 \) is not less than \( 3 \) (it is equal), the inequality does not hold. Thus, \((0, 3)\) is not a solution.

Answer:

b. \((-4, 5)\)