Solve a system of equations using substitution: word problems

Learning Objectives Define variables based on the context of a word problem. Translate verbal descriptions from word problems into a system of two linear equations. Apply the substitution method to solve a system of linear equations derived from a word problem. Interpret the solution of a system of equations in the context of the original word problem. Check the validity of their solution by substituting values back into the original equations and problem statement. Identify and correct common errors when solving word problems using substitution. Ever wonder how stores figure out how many of each item to order, or how much change to give you when you buy multiple things? 💰 Systems of equations help us solve these real-world puzzles! In this lesson, you'll learn how to...

TermDefinitionExample System of Linear EquationsA set of two or more linear equations that share the same variables. The goal is to find values for the variables that satisfy all equations simultaneously.$\{x + y = 10 \newline x - y = 2\}$ VariableA symbol, usually a letter (like $x$ or $y$), that represents an unknown quantity in an equation or expression.In the problem 'The sum of two numbers is 15', we can let $x$ be the first number and $y$ be the second number. Word ProblemA mathematical problem presented in a narrative or story format, requiring translation into mathematical equations to be solved.Sarah bought 3 apples and 2 bananas for $5. Mark bought 1 apple and 4 bananas for $4. How much does each fruit cost? Substitution MethodAn algebraic technique for solving systems...

Steps for Solving Word Problems with Substitution 1. Define variables. 2. Write two equations. 3. Solve one equation for one variable. 4. Substitute into the other equation. 5. Solve for the remaining variable. 6. Substitute back to find the first variable. 7. Check your solution. This is the general procedure to follow when tackling any word problem that requires solving a system of equations using the substitution method. Substitution Rule If $y = ext{expression}$ (or $x = ext{expression}$), then you can replace $y$ (or $x$) with that expression in any other equation. This rule is the core of the substitution method. It allows you to reduce a system of two equations with two variables into a single equation with one variable, which is easier to solve. Checking Your S...