In Exercises 35-46, determine which, if any, of the ordered pairs listed satisfy the given equat

step 1 So for this question, we're giving the following equation 6x minus 4 y minus 8 is equal to 0. An

In Exercises 35-46, determine which, if any, of the ordered...

Key Concepts

Substitution Method for Verification

The substitution method involves replacing the variables in an equation with specific values from an ordered pair to verify if the equation is satisfied. If, after substitution, the resulting expression is a true statement (typically yielding equality), then the ordered pair is a solution to the equation.

Solution Set Verification

Verifying a solution set is a fundamental procedure in algebra, ensuring that proposed solutions indeed satisfy the given equation. This is especially important when multiple potential solutions are provided, as each must be independently confirmed by checking whether the calculated result matches the equation's requirements.

Linear Equations

A linear equation represents a straight line in the coordinate plane and is typically written in the form Ax + By + C = 0. Understanding the structure of a linear equation is crucial, as it allows one to determine the relationship between the x and y variables, identify the slope and intercepts, and analyze the behavior of the line.

Ordered Pairs

An ordered pair consists of two numbers, typically representing the coordinates (x, y) of a point in the plane. In the context of linear equations, each ordered pair is evaluated to see if it satisfies the equation, meaning that when the coordinates are substituted into the equation, the equality holds true.

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