options: Perform arithmetic operations on polynomials.

Analyze patterns and relationships.

Add and subtract within 20.

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

Work with addition and subtraction equations.

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

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

Write expressions in equivalent forms to solve problems.

Write and interpret numerical expressions.

Understand the relationship between zeros and factors of polynomials.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Work with radicals and integer exponents.

Represent and solve problems involving addition and subtraction.

Represent and analyze quantitative relationships between dependent and independent variables.

Use properties of operations to generate equivalent expressions.

Gain familiarity with factors and multiples.

Use polynomial identities to solve problems.

Solve equations and inequalities in one variable.

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

Understand the connections between proportional relationships, lines, and linear equations.

Interpret the structure of expressions.

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

Create equations that describe numbers or relationships

Represent and solve equations and inequalities graphically.

Solve systems of equations.

Multiply and divide within 100.

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

Use the four operations with whole numbers to solve problems.

Generate and analyze patterns.

Represent and solve problems involving multiplication and division.

Reason about and solve one-variable equations and inequalities.

Rewrite rational expressions.

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

Understand solving equations as a process of reasoning and explain the reasoning.
problem_activity: Task
Lisa is working with the system of equations $x + 2y = 7$ and $2x - 5y = 5$. She multiplies the first equation by 2 and then subtracts the second equation to find $9y = 9$, telling her that $y = 1$. Lisa then finds that $x = 5$. Thinking about this procedure, Lisa wonders
There are lots of ways I could go about solving this problem. I could add 5 times the first equation and twice the second or I could multiply the first equation by -2 and add the second. I seem to find that there is only one solution to the two equations but I wonder if I will get the same solution if I use a different method?
What is the answer to Lisa's question? Explain.
Does the answer to (a) change if we have a system of two equations in two unknowns with no solutions? What if there are infinitely many solutions?


correct_option_index: 24