Find a value using two-variable equations

Learning Objectives Identify two variables and their relationship in a given scenario. Translate a simple real-world problem into a two-variable equation. Substitute a known numerical value for one variable into an equation. Solve the resulting one-variable equation to find the value of the unknown variable. Check the solution by substituting both values back into the original equation. Explain how two quantities are related using an equation. Have you ever wondered how much money you'd earn if you worked for a certain number of hours, or how many cookies you can bake with a specific amount of flour? 🍪 Let's find out how math helps us solve these puzzles! In this lesson, you'll learn how to work with equations that have two different changing numbers, called...

TermDefinitionExample VariableA letter (like $x$, $y$, $C$, or $H$) that stands for a number we don't know yet, or a number that can change.In the equation $C = 2A$, 'C' (cost) and 'A' (number of apples) are variables. EquationA mathematical sentence that shows two expressions are equal, using an equals sign (=).$5 + 3 = 8$ is an equation. $C = 2A$ is also an equation. Two-Variable EquationAn equation that contains two different variables, showing how they are related.$y = x + 5$ or $D = 60T$ are examples of two-variable equations. SubstitutionThe act of replacing a variable with a specific number or expression.If $x=3$ in the equation $y = x + 5$, you substitute 3 for $x$ to get $y = 3 + 5$. EvaluateTo find the numerical value of an expression or equation by perf...

Substitution Principle If $y = f(x)$ and $x = a$, then $y = f(a)$. This rule allows you to replace one of the variables in a two-variable equation with its known numerical value. This turns the equation into a simpler one-variable equation that you can solve. Solving for the Unknown To solve $A + B = C$ for $A$, subtract $B$ from both sides: $A = C - B$. To solve $AB = C$ for $A$, divide both sides by $B$: $A = \frac{C}{B}$. After substituting, you'll have an equation with only one unknown variable. Use inverse operations (like subtracting to undo addition, or dividing to undo multiplication) to get the unknown variable by itself on one side of the equals sign. Verification Rule If you found $x_0$ for $y_0$ in $y = f(x)$, check if $y_0 = f(x_0)$ is true. Always...