Find a value using two-variable equations

Learning Objectives Define and identify a two-variable equation. Substitute a given numerical value for one variable into a two-variable equation. Solve the resulting one-variable equation to find the value of the unknown variable. Check their solution by substituting both values back into the original equation. Interpret solutions to two-variable equations in real-world contexts. Represent solutions as ordered pairs (x, y). Have you ever wondered how stores calculate your total bill based on how many items you buy? 🛒 Or how a recipe tells you how much of one ingredient you need if you change another? 🤔 In this lesson, you'll learn how to work with equations that have two unknown numbers, called variables. We'll discover how to find the value of one variable whe...

TermDefinitionExample Two-Variable EquationAn equation that contains two different unknown quantities, usually represented by letters like 'x' and 'y'.y = 2x + 5 (Here, 'x' and 'y' are the two variables.) VariableA symbol, usually a letter, that represents an unknown or changing numerical value.In the equation '3a + b = 10', 'a' and 'b' are variables. SubstitutionThe process of replacing a variable with a known numerical value or another expression.If y = x + 3 and you know x = 4, you substitute 4 for x to get y = 4 + 3. Solution (of a Two-Variable Equation)A pair of values (one for each variable) that makes the equation true when substituted into it.For y = x + 3, the pair (2, 5) is a solution because 5 = 2 + 3 is true...

The Substitution Principle If you know the value of one variable in a two-variable equation, you can replace that variable with its known value. This rule allows you to turn a two-variable equation into a one-variable equation that you already know how to solve. For example, if you have $y = 3x + 1$ and you know $x = 2$, you can substitute 2 for $x$ to get $y = 3(2) + 1$. Solving for the Unknown Variable After substitution, use inverse operations to isolate the remaining unknown variable on one side of the equation. Remember to perform operations like addition, subtraction, multiplication, and division to both sides of the equation to keep it balanced. For example, if you have $10 = 2x + 4$, you would subtract 4 from both sides, then divide by 2 to find $x$. Checking You...