Does (x, y) satisfy an equation?

Learning Objectives Identify the x and y values in a given ordered pair. Define what it means for an ordered pair to 'satisfy' an equation. Accurately substitute numerical values for variables into a two-variable equation. Evaluate both sides of an equation after substitution using the order of operations. Determine if an ordered pair satisfies an equation by comparing the evaluated sides. Clearly state whether an ordered pair makes an equation true or false. Ever wonder if a secret code works or if a key fits a lock? 🕵️‍♀️ In math, we'll learn how to check if a pair of numbers 'fits' an equation perfectly! In this lesson, you'll discover how to test if specific pairs of numbers, called ordered pairs (x, y), make an equation true. This skill is...

TermDefinitionExample EquationA mathematical statement that shows two expressions are equal, usually with an equals sign (=) in between.$$x + 5 = 12$$ Two-variable equationAn equation that contains two different unknown values, represented by variables (most commonly 'x' and 'y').$$y = x + 3$$ VariableA symbol, usually a letter, that represents an unknown number or a quantity that can change.In $$y = x + 3$$, 'x' and 'y' are variables. Ordered Pair (x, y)A pair of numbers written in a specific order, usually representing a point on a graph. The first number is always the x-value, and the second is always the y-value.$$(2, 7)$$ means that $$x=2$$ and $$y=7$$. SubstituteTo replace a variable in an equation with a specific numerical value.If $$x=4$$, y...

The Substitution Principle To check if an ordered pair $(x, y)$ satisfies an equation, replace each variable in the equation with its corresponding numerical value from the ordered pair. This is the first step! Always put the x-value where 'x' is and the y-value where 'y' is. For example, if you have $(3, 8)$ and the equation $y = x + 5$, you would write $8 = 3 + 5$. The Equality Check After substituting the values and simplifying both sides of the equation, if the left side of the equation equals the right side, the ordered pair satisfies the equation. If they are not equal, it does not. Once you've done the math on both sides, compare them. If $Left Side = Right Side$, then your ordered pair is a solution. If $Left Side \neq Right Side$, it's...