# Understand Systems of Equations

Related Topics:
Common Core (Algebra)
Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students learn how to prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

Common Core: HSA-REI.C.5

Understanding systems of equations in two variables
Common Core Standard in Algebra, REI.5
Understand why adding multiples of equations in systems of two equations and two variables gives an equivalent equation.
Solving Systems of Equations Using Multiplication (A-REI.5)
How to solve systems of equations by using multiplication?
Example:
Each family in a neighborhood is contributing \$25 worth of food to the neighborhood picnic? The Kennedy family is bringing 15 packages of buns. Hamburger buns cost \$2.00 per package. Hot-dog buns cost \$1.50 per package. How many packages of each type of bun do they have?

Understanding systems of equations example.
Example:
You are at a Parisian cafe with a friend. A local in front of you buys a cup of coffee and a croissant for 5.30 Euro. When you and your friend get 2 cups of coffee and 2 croissants, you are charged 14 Euro.
Can we solve for the price of a cup of coffee and a croissant using this information in a system of linear equations in two variables? If yes, what is the solution? If no, what is the reason we cannot?
Understanding systems of equations example 2.
You are solving a system of linear equations in two variables. You have found more than one solution that satisfies the system. Which of the following statements are true?

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