Solve a system of equations using substitution

Learning Objectives Identify two unknown quantities in a consumer math word problem. Recognize a relationship where one unknown quantity is described in terms of another. Use the substitution strategy to simplify a problem involving two unknown quantities. Calculate the value of one unknown quantity after substitution. Use the value of one unknown to find the value of the second unknown quantity. Check their solutions by plugging the found values back into the original problem descriptions. Have you ever wondered how stores figure out how many of each item to order when they know how many total items they sold, but one item is more popular? 🤔 It's like a math detective game! In this lesson, you'll learn a clever strategy called 'substitution' to solve t...

TermDefinitionExample Unknown QuantityA number or value that we don't know yet and need to find in a problem.In 'You bought apples and bananas,' the number of apples and the number of bananas are unknown quantities. RelationshipHow two unknown quantities are connected or compared to each other.If 'you bought 3 more apples than bananas,' this describes a relationship between the number of apples and bananas. TotalThe sum or combined amount of two or more quantities or values.If 'you spent $10 total on apples and bananas,' $10 is the total cost. SubstitutionReplacing one unknown quantity with an equivalent description or value from another part of the problem.If 'apples = bananas + 3', then in a total calculation, you can replace 'apples&#03...

Identify the Unknowns and Their Relationship Look for two things you need to find. Then, find a sentence that tells you how one unknown is described using the other. This is the first step to understand what you're looking for and how the pieces connect. For example, 'The cost of a pen is $0.50 more than the cost of a pencil.' Substitute the Relationship into the Total Replace the description of one unknown into the statement about the total amount or quantity. If you know 'Pen cost = Pencil cost + $0.50', and 'Total cost = Pen cost + Pencil cost', you can change the total cost statement to 'Total cost = (Pencil cost + $0.50) + Pencil cost'. This makes it easier to solve. Solve for the First Unknown After substituting, you w...