options: Work with radicals and integer exponents.

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

Gain familiarity with factors and multiples.

Multiply and divide within 100.

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

Use the four operations with whole numbers to solve problems.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Represent and solve problems involving multiplication and division.

Write expressions in equivalent forms to solve problems.

Generate and analyze patterns.

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

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

Use properties of operations to generate equivalent expressions.

Understand the relationship between zeros and factors of polynomials.

Represent and solve equations and inequalities graphically.

Add and subtract within 20.

Perform arithmetic operations on polynomials.

Reason about and solve one-variable equations and inequalities.

Rewrite rational expressions.

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

Use polynomial identities to solve problems.

Solve equations and inequalities in one variable.

Work with addition and subtraction equations.

Represent and solve problems involving addition and subtraction.

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

Write and interpret numerical expressions.

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

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

Solve systems of equations.

Create equations that describe numbers or relationships

Analyze patterns and relationships.

Interpret the structure of expressions.
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: 30