Question

Choose the statement below correctly describing a solution of an inequality in two variables.

A. An ordered pair is a solution of an inequality in two variables if it is in the form (x, y).
B. An ordered pair is a solution of an inequality in two variables if replacing the variables by the values of the ordered pair results in a false statement.
C. A single number is a solution of an inequality in two variables if replacing the variables by this number results in a true statement.
D. An ordered pair is a solution of an inequality in two variables if replacing the variables by the values of the ordered pair results in a true statement.

Answer 1

The correct statement is D, which states that an ordered pair is a solution to an inequality if it makes the inequality true when substituted for the variables.

Step-by-step explanation:

The correct statement describing a solution of an inequality in two variables is: D. An ordered pair is a solution of an inequality in two variables if replacing the variables by the values of the ordered pair results in a true statement. This means that if you have an inequality, such as y > 2x + 3, and you plug in the x and y values from your ordered pair, the inequality should hold true. For example, the pair (1, 5) would be a solution because when we replace x with 1 and y with 5, we get 5 > 2(1) + 3, which simplifies to 5 > 5, not a true statement, thus (1, 5) is not a solution. However, (2, 5) would be a solution because 5 > 2(2) + 3, which simplifies to 5 > 7, also not true.