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Questions and Answers
The point (0,1) satisfies the inequality $3x + 2y ≥ 5$.
The point (0,1) satisfies the inequality $3x + 2y ≥ 5$.
False
The ordered pair (-3, 2) can be tested in the inequality $2x - y$.
The ordered pair (-3, 2) can be tested in the inequality $2x - y$.
True
Substituting (0,1) into the expression $3x + 2y$ yields a result of 5.
Substituting (0,1) into the expression $3x + 2y$ yields a result of 5.
False
The expression $2x - y$ can be positive, negative, or zero depending on the values of x and y.
The expression $2x - y$ can be positive, negative, or zero depending on the values of x and y.
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The result of $3(0) + 2(1)$ is greater than or equal to 5.
The result of $3(0) + 2(1)$ is greater than or equal to 5.
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Study Notes
Determining Solutions to Inequalities
- To determine if an ordered pair is a solution to an inequality, substitute the x and y values into the inequality.
- If the resulting inequality is true, the ordered pair is a solution. If it's false, it's not a solution.
Example 1: 3x + 2y ≥ 5 and (0, 1)
- Substitute x = 0 and y = 1 into the inequality: 3(0) + 2(1) ≥ 5
- Simplify: 2 ≥ 5
- Since 2 is not greater than or equal to 5, (0, 1) is not a solution.
Example 2: 2x - y and (-3, 2)
- The inequality is incomplete. To determine if (-3, 2) is a solution, the complete inequality is needed.
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Description
Test your understanding of how to determine solutions to inequalities with this quiz. You'll learn to substitute values into inequalities and evaluate if ordered pairs are solutions. Practice with examples and deepen your math skills!
