To solve the question of finding which ordered pair makes both inequalities true, we need to examine each ordered pair against both inequalities:
1. The first inequality is [tex]\( y > -2x + 3 \)[/tex].
2. The second inequality is [tex]\( y \leq x - 2 \)[/tex].
Let's test each ordered pair:
Ordered Pair (0,0):
1. For [tex]\( y = 0 \)[/tex] and [tex]\( x = 0 \)[/tex]:
- Check the first inequality: [tex]\( 0 > -2(0) + 3 \)[/tex] which simplifies to [tex]\( 0 > 3 \)[/tex]. This statement is false.
- Since the first inequality is not satisfied, we do not need to check the second one.
Ordered Pair (0,-1):
1. For [tex]\( y = -1 \)[/tex] and [tex]\( x = 0 \)[/tex]:
- Check the first inequality: [tex]\( -1 > -2(0) + 3 \)[/tex] which simplifies to [tex]\( -1 > 3 \)[/tex]. This statement is false.
- Since the first inequality is not satisfied, we do not need to check the second one.
Ordered Pair (1,1):
1. For [tex]\( y = 1 \)[/tex] and [tex]\( x = 1 \)[/tex]:
- Check the first inequality: [tex]\( 1 > -2(1) + 3 \)[/tex] which simplifies to [tex]\( 1 > 1 \)[/tex]. This statement is false.
- Since the first inequality is not satisfied, we do not need to check the second one.
After checking all ordered pairs against the inequalities, we find that none of the pairs satisfy both inequalities simultaneously. Therefore, none of the given ordered pairs make both inequalities true.
The solution is:
[tex]\[ \boxed{\text{None of the given ordered pairs}} \][/tex]
