options: Generate and analyze patterns.

Gain familiarity with factors and multiples.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Use properties of operations to generate equivalent expressions.

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

Solve equations and inequalities in one variable.

Represent and solve problems involving multiplication and division.

Reason about and solve one-variable equations and inequalities.

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

Work with radicals and integer exponents.

Represent and solve equations and inequalities graphically.

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

Perform arithmetic operations on polynomials.

Multiply and divide within 100.

Use the four operations with whole numbers to solve problems.

Use polynomial identities to solve problems.

Rewrite rational expressions.

Add and subtract within 20.

Create equations that describe numbers or relationships

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

Interpret the structure of expressions.

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

Work with addition and subtraction equations.

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

Write and interpret numerical expressions.

Write expressions in equivalent forms to solve problems.

Solve systems of equations.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Represent and solve problems involving addition and subtraction.

Understand the relationship between zeros and factors of polynomials.

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

Analyze patterns and relationships.
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: 27