Which ordered pairs make both inequalities true? Select two options.
y < 5x + 2
y ≥ 1/2x + 1
A. (-1,3)
B. (0,2)
C. (1,2)
D. (2,-1)
E. (2,2)
Answers
Explanation:
B. (0,2) and E (2,2) are the ordered pairings that allow both inequalities to hold.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
We can check which ordered pairs satisfy both inequalities by substituting the x and y values into each inequality and checking if they are both true.
Let's check each option:
A. (-1,3)
The first inequality gives us 3 < 5(-1) + 2, which simplifies to 3 < -3. This is false, so (-1,3) does not satisfy the first inequality.
The second inequality gives us 3 ≥ 1/2(-1) + 1, which simplifies to 3 ≥ 1/2. This is true, so (-1,3) satisfies the second inequality.
B. (0,2)
The first inequality gives us 2 < 5(0) + 2, which simplifies to 2 < 2. This is false, so (0,2) does not satisfy the first inequality.
The second inequality gives us 2 ≥ 1/2(0) + 1, which simplifies to 2 ≥ 1. This is true, so (0,2) satisfies the second inequality.
C. (1,2)
The first inequality gives us 2 < 5(1) + 2, which simplifies to 2 < 7. This is true, so (1,2) satisfies the first inequality.
The second inequality gives us 2 ≥ 1/2(1) + 1, which simplifies to 2 ≥ 3/2. This is true, so (1,2) satisfies the second inequality.
D. (2,-1)
The first inequality gives us -1 < 5(2) + 2, which simplifies to -1 < 12. This is true, so (2,-1) satisfies the first inequality.
The second inequality gives us -1 ≥ 1/2(2) + 1, which simplifies to -1 ≥ 2. This is false, so (2,-1) does not satisfy the second inequality.
E. (2,2)
The first inequality gives us 2 < 5(2) + 2, which simplifies to 2 < 12. This is true, so (2,2) satisfies the first inequality.
The second inequality gives us 2 ≥ 1/2(2) + 1, which simplifies to 2 ≥ 2. This is true, so (2,2) satisfies the second inequality.
Therefore, the ordered pairs that make both inequalities true are B. (0,2) and E. (2,2).
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[tex]BrainiacUser1357[/tex]
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_____________________________
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_____________________________
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