Math - 2018-19
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.
- 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)
· Properties of Equality:
Multiplicative Property of Zero
Zero Product Property
Transitive Property of Equality
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
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.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
A.4d2 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.4d1 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.4d3 Solve and confirm algebraic solutions to a system of two linear equations using a graphing utility.
whether a system of two linear equations has one, an infinite number, or no
a system of two linear equations that models a practical situation.
and determine the reasonableness of
the algebraic or graphical solution of a system of two linear equations that
models a practical situation.
· A.4e3 Solve practical problems involving equations and systems of equations.
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