Which ordered pair makes both inequalities true?
[tex]
\begin{array}{l}
y \leq-x+1 \\
y\ \textgreater \ x
\end{array}
[/tex]
Answer (1)
Substitute each ordered pair into the inequalities.
Check if both inequalities are true for the given ordered pair.
The ordered pair (0, 1) satisfies both inequalities: 1 ≤ − 0 + 1 and 0"> 1 > 0 .
Therefore, the ordered pair that makes both inequalities true is ( 0 , 1 ) .
Explanation
Understanding the problem We are given two inequalities: y y > x We need to find an ordered pair $(x, y)$ that satisfies both inequalities. Let's test the given options. 2. Testing (0, 0) Let's test the ordered pair $(0, 0)$. Substituting $x = 0$ and $y = 0$ into the inequalities, we get: 0 0"> 0 > 0 The first inequality is true, but the second inequality is false. Therefore, ( 0 , 0 ) is not a solution.
Testing (1, 1) Let's test the ordered pair ( 1 , 1 ) .
Substituting x = 1 and y = 1 into the inequalities, we get: 1 1 > 1 Both inequalities are false. Therefore, $(1, 1)$ is not a solution. 4. Testing (0, 1) Let's test the ordered pair $(0, 1)$. Substituting $x = 0$ and $y = 1$ into the inequalities, we get: 1 0"> 1 > 0 Both inequalities are true. Therefore, ( 0 , 1 ) is a solution.
Testing (1, 0) Let's test the ordered pair ( 1 , 0 ) .
Substituting x = 1 and y = 0 into the inequalities, we get: 0 0 > 1 The first inequality is true, but the second inequality is false. Therefore, ( 1 , 0 ) is not a solution.
Final Answer The ordered pair that makes both inequalities true is ( 0 , 1 ) .
Examples
Understanding inequalities is crucial in various real-life scenarios, such as determining budget constraints or setting acceptable ranges for measurements. For instance, if you're planning a party and have a limited budget, you can use inequalities to ensure your expenses stay within your financial limits. Similarly, in manufacturing, inequalities help maintain product quality by setting tolerance levels for dimensions and other parameters. By mastering inequalities, you can make informed decisions and optimize outcomes in everyday situations.
