Ch. 1 - Equations and Inequalities

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo

Blitzer 8th Edition

Ch. 1 - Equations and Inequalities

Problema 74a

Capitolo 2, Problema 74a

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The ordered pair (2, 5) satisfies 3y - 2x = - 4.

Guida verificata passo dopo passo

Step 1: Recall that an ordered pair (x, y) satisfies an equation if substituting x and y into the equation results in a true statement.

Step 2: Identify the given ordered pair (2, 5), where x = 2 and y = 5, and the equation 3y - 2x = -4.

Step 3: Substitute x = 2 and y = 5 into the equation. Replace y with 5 and x with 2, resulting in 3(5) - 2(2) = -4.

Step 4: Simplify the left-hand side of the equation. First, calculate 3(5) and 2(2), then subtract the results.

Step 5: Compare the simplified left-hand side to the right-hand side (-4). If they are equal, the statement is true; otherwise, it is false. If false, adjust the equation or ordered pair to make it true.

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Ordered Pairs

An ordered pair consists of two elements, typically represented as (x, y), where 'x' is the first element and 'y' is the second. In the context of a function or equation, ordered pairs are used to represent points on a coordinate plane, allowing us to evaluate whether a specific point satisfies a given equation.

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Substitution in Equations

Substitution is the process of replacing variables in an equation with specific values to determine the truth of a statement. In this case, substituting the values from the ordered pair (2, 5) into the equation 3y - 2x = -4 allows us to check if the equation holds true for those values.

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Linear Equations

A linear equation is an equation that represents a straight line when graphed on a coordinate plane. It typically takes the form Ax + By = C, where A, B, and C are constants. Understanding the properties of linear equations is essential for determining whether specific points lie on the line represented by the equation.

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