Question

If 2x-y>=-2, and y-x>=-4, which of the following must be true?

a. (0,0)
b. (-5,4)
c. (10,10)
d. (10,6)

Answer 1

The coordinate pairs (0,0) and (10,6) satisfy both inequalities 2x - y ≥ -2 and y - x ≥ -4. Therefore, both points must be true among the given options.

Step-by-step explanation:

Verifying the Ordered Pairs

We can begin by testing each of the coordinate pairs to see which one satisfies both inequalities given in the question: 2x - y ≥ -2 and y - x ≥ -4.

1. For point (0,0), substituting x and y with 0, we get:
   
   2(0) - 0 ≥ -2 (True)
   
   0 - 0 ≥ -4 (True)
2. For point (-5,4), substituting x = -5 and y = 4, we get:
   
   2(-5) - 4 ≥ -2 (False)
   
   4 - (-5) ≥ -4 (True)
   
   This pair does not satisfy the first inequality.
3. For point (10,10), substituting x = 10 and y = 10, we get:
   
   2(10) - 10 ≥ -2 (True)
   
   10 - 10 ≥ -4 (True)
4. For point (10,6), substituting x = 10 and y = 6, we get:
   
   2(10) - 6 ≥ -2 (True)
   
   6 - 10 ≥ -4 (True)

Based on the substitutions, both point (0,0) and point (10,6) satisfy both inequalities and must be true, according to the given options.