few_shots: Example:
Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Mathematical concept/skill options: 
A. Analyze proportional relationships and use them to solve real-world and mathematical problems.
B. Understand ratio concepts and use ratio reasoning to solve problems.


Your response:
B

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_000972

6
options: Perform arithmetic operations on polynomials.

Solve systems of equations.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Rewrite rational expressions.

Understand properties of multiplication and the relationship between multiplication and division.

Analyze patterns and relationships.

Represent and solve problems involving multiplication and division.

Use the four operations with whole numbers to solve problems.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Represent and solve problems involving addition and subtraction.

Understand solving equations as a process of reasoning and explain the reasoning.

Understand the relationship between zeros and factors of polynomials.

Multiply and divide within 100.

Add and subtract within 20.

Create equations that describe numbers or relationships

Represent and solve equations and inequalities graphically.

Reason about and solve one-variable equations and inequalities.

Write and interpret numerical expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Gain familiarity with factors and multiples.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Understand and apply properties of operations and the relationship between addition and subtraction.

Solve equations and inequalities in one variable.

Work with equal groups of objects to gain foundations for multiplication.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Generate and analyze patterns.

Write expressions in equivalent forms to solve problems.

Use polynomial identities to solve problems.

Work with addition and subtraction equations.

Interpret the structure of expressions.

Use properties of operations to generate equivalent expressions.

Work with radicals and integer exponents.

Understand the connections between proportional relationships, lines, and linear equations.
problem_activity: Problem 1
Without solving the systems, explain why the following system must have the same solution.
| System 1:                       $${4x-5y=13 }$$                        $${3x+6y=11}$$ | System 2:                       $${8x-10y=26}$$                        $${x-11y=2}$$ |
|---------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------|
Problem 2
Solve the system of equations by writing a new system that eliminates one of the variables.
$${3x+2y=4}$$
$${4x+7y=1}$$


correct_option_index: 1