Ch. 1 - Equations and Inequalities

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 1 - Equations and Inequalities

Problem 74a

Chapter 2, Problem 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.

Verified step by step guidance

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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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.

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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