#### Math - 2019-20

# A.4de - Systems of Linear Equations

A.4The student willsolved) systems of two linear equations in two variables algebraically and graphically;

e) practical problems involving equations and systems of equations.

*Adopted: 2016*

### 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

· 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 Addition

Associative Property of Multiplication

Commutative Property of Addition

Commutative Property of Multiplication

Identity Property of Addition (Additive Identity)

Identity Property of Multiplication (Multiplicative Identity)

Inverse Property of Addition (Additive Inverse) 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

Addition 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.4d_{2 }Given 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.4d_{1 }Given 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.4d_{3 }**Solve**
and **confirm** algebraic solutions to a
system of two linear equations using a graphing utility.

·
A.4d_{4 }**Determine**
whether a system of two linear equations has one, an infinite number, or no
solutions.

·
A.4e_{1 }**Write**
a system of two linear equations that models a practical situation.

·
A.4e_{2 }**Interpret**
and **determine** the reasonableness of
the algebraic or graphical solution of a system of two linear equations that
models a practical situation.

·
A.4e_{3 }**Solve**
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: Jul 30, 2019*