Unit 4

Common Core Standards Covered

• 8.EE.C.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously
• 8.EE.C.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
• 8.EE.C.8c Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.*

Unit Vocabulary

Coefficient: The number that is multiplied by the variable in an algebraic expression.

Distributive Property: For all real numbers a, b, and c, a(b + c) = ab + ac, and a(b - c) = ab - ac.

Elimination: A method for solving systems of equations in which equations are added or subtracted.

Equivalent Relations: Expressions that have the same value for all values of the variables.

*Infinitely Many Solutions: When two lines are the same; When any point is a solution to both equations in a system.

Intersection: Lines that have one and only one point in common.

Linear Equations: An equation whose solutions form a straight line on a coordinate plane.

Point of Intersection: The point where two lines meet

*No Solution: When two lines are parallel

*One Solution: A value or values that make an equation true.

solution area

Solutions: A set of values that make all equations in a system true.

*Substitution: To replace a variable with a number or another expression in an algebraic expression. Also a method for solving a system of equations by substituting an expression for a variable in another equation.

*Systems of Equations: A set of two or more equations that contain two or more variables.

systems of Inequalities:

Variables: symbols used to represent a quantities that can change.

MODELING & REASONING

For MODELING, emphasize:

• Constructing an accurate mathematical model to represent and explain a concept or a real-world problem/situation given in a prompt.
  • Examples of models used in this unit include graphic and algebraic systems of linear equations, pictorial representations, verbal descriptions, and digital manipulatives.
• Using a given linear model to predict or identify solution(s) to a system of linear equations.

For REASONING, emphasize:

• Accurately explaining or showing one’s own work to support an answer
  • Look for: “Show or explain…”
• Constructing accurate and complete justifications of one’s own work
  • Look for: “Justify…”
• Constructing complete arguments to support or refute the claims of others
  • Look for: “Provide work or an explanation to justify whether or not the student’s claim is correct.”