Does (x, y) satisfy the equation?

Learning Objectives Define what an ordered pair (x, y) represents in the context of an equation. Identify the x and y values within a given ordered pair. Substitute the values of x and y from an ordered pair into a two-variable equation. Evaluate both sides of an equation after substitution. Determine if an ordered pair is a solution to a two-variable equation by checking for equality. Explain the meaning of an ordered pair satisfying an equation. Ever wonder if a specific point on a map 🗺️ fits a certain path or rule? In math, we can check if a pair of numbers fits an equation! In this lesson, you'll learn how to determine if a given pair of numbers, called an ordered pair (x, y), makes a two-variable equation true. This skill is fundamental for understanding how equa...

TermDefinitionExample Two-variable equationAn equation that contains two different variables, usually 'x' and 'y', representing unknown quantities.$y = 2x + 1$ Ordered pairA pair of numbers (x, y) that represents a single point or a specific set of values for the variables x and y, where the order matters.$(3, 7)$ Solution to an equationAn ordered pair (x, y) that makes a two-variable equation true when its values are substituted for the variables.For $y = x + 1$, $(2, 3)$ is a solution because $3 = 2 + 1$ is true. SubstituteTo replace a variable in an equation with a specific numerical value.In $y = x + 1$, substituting $x=2$ means $y = 2 + 1$. VariableA symbol, usually a letter, that represents a quantity that can change or take on different values.In $y = 2x + 1$, &...

Ordered Pair Structure An ordered pair is always written as $(x, y)$, where the first value is the x-coordinate and the second value is the y-coordinate. This rule defines how to correctly identify which number corresponds to which variable when substituting into an equation. The Substitution and Check Rule To check if an ordered pair $(x, y)$ satisfies an equation, substitute the x-value for 'x' and the y-value for 'y' into the equation. Then, simplify both sides of the equation to see if the resulting statement is true (e.g., $5 = 5$). This is the fundamental process for determining if an ordered pair is a solution. If the statement is true, the ordered pair satisfies the equation; if false, it does not. Definition of 'Satisfy' An ordere...