# A.4de - Systems of Linear Equations

A.4  The student will solve

d)  systems of two linear equations in two variables algebraically and graphically;

e)  practical problems involving equations and systems of equations.

### BIG IDEAS

• I can find how far and how fast a bus travels, the number of fruits that can be purchased, and how long it takes to drain a swimming pool.
• I will be able to write symbolic representations of the way numbers behave and will know that in order to maintain equality, an operation performed on one side must also be performed on the other side.

### UNDERSTANDING THE STANDARD

2016 VDOE Curriculum Framework - AI.4 Understanding

·  A solution to an equation is the value or set of values that can be substituted to make the equation true.

·  Each point on the graph of a linear or quadratic equation in two variables is a solution of the equation.

·  Practical problems may be interpreted, represented, and solved using linear and quadratic equations.

·  The process of solving linear and quadratic equations can be modeled in a variety of ways, using concrete, pictorial, and symbolic representations.

·  Properties of real numbers and properties of equality are applied to solve equations.

·  Properties of Real Numbers:

­  Associative Property of Multiplication

­  Commutative Property of Multiplication

­  Identity Property of Multiplication (Multiplicative Identity)

­  Inverse Property of Multiplication (Multiplicative Inverse)

­  Distributive Property

·  Properties of Equality:

­  Multiplicative Property of Zero

­  Zero Product Property

­  Reflexive Property

­  Symmetric Property

­  Transitive Property of Equality

­  Subtraction Property of Equality

­  Multiplication Property of Equality

­  Division Property of Equality

­  Substitution

·  A system of linear equations with exactly one solution is characterized by the graphs of two lines whose intersection is a single point, and the coordinates of this point satisfy both equations.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

·  A.4dGiven a system of two linear equations in two variables that has a unique solution, solve the system graphically by identifying the point of intersection.

·  A.4dGiven a system of two linear equations in two variables that has a unique solution, solve the system by substitution or elimination to identify the ordered pair which satisfies both equations.

·  A.4dSolve and confirm algebraic solutions to a system of two linear equations using a graphing utility.

·  A.4dDetermine whether a system of two linear equations has one, an infinite number, or no solutions.

·  A.4eWrite a system of two linear equations that models a practical situation.

·  A.4eInterpret and determine the reasonableness of the algebraic or graphical solution of a system of two linear equations that models a practical situation.

·  A.4eSolve practical problems involving equations and systems of equations.

### KEY VOCABULARY

literal equation (formula), expression, equation, properties of real numbers, properties of equality, quadratic equation, quadratic function, quadratic expression, roots, zeros, linear equation, system, substitution, elimination, ordered pair, coordinate, intersection, intercepts, solution, infinite, parallel, coincide, simultaneous

Updated: Aug 23, 2018