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Intro to systems

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Systems of equations: trolls, tolls (1 of 2)

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A troll forces us to use algebra to figure out the make-up of his currency. We end up setting up a system of equations.

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What does it mean to be a solution to a system
of equations?

Does the intersection of the two lines satisfy the two equations?

How do you solve a system of equations?

What is a real-world application of systems?
How do businesses use systems of equations to
maximize profits?

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We will use our knowledge of graphing to graph a system of equations.

We will interpret the intersection point of the graph of the system algebraically.

We will use slope-intercept form to derive the equations of the lines that comprise the system.

We will be able to match a given system to a graph or a graph to a system of equations.

We will use substitution to verify that an ordered pair is a solution to a system.

We will use elimination to solve a system of equations

We will use the substitution method to solve a system of equations.

We will correctly interpret the result obtained by solving a system of equations with infinitely many solutions.

We will correctly interpret the results obtained by solving a system of equations with no solution.

We will be able to explain the relationship of the result of solving a system with one, infinitely many, or no solutions with their graphs.

We will be able to solve simple systems by inspection.

We will use our knowledge of solving equations to solve real-world and mathematical
problems leading to linear equations in two variables.

We will solve word problems that can lead to equations of the form px + q = r and p(x + q) =r, where p, q, and r are specific rational numbers.

We will reason about real-world situation to create a system of equations that represent the situation.

We will use our understanding of systems of equations to write the solution in context of the problem.

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PRIORITY STANDARDS
EE.8​ Analyze and solve pairs of simultaneous linear equations.
a​) 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.
b)​ 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.
c​) Solve real-world and mathematical problems leading to 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.

SUPPORTING STANDARDS
EE.5​ Graph proportional relationships, interpreting the unit rate as the slope of the graph.
Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving
objects has greater speed.

F.2 ​Compare properties of two functions each represented in a different way (algebraically,
graphically, numerically in tables, or by verbal descriptions). For example, given a linear
function represented by a table of values and a linear function represented by an algebraic
expression, determine which function has the greater rate of change.

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Interpret
Solve
Justify
Refute
Construct
Chain of reason
Argument
Conclude
Corroborate
Evidence
Confirm
Verify
Create
Apply
Model

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Proportional
Relationship
Direct Variation
Slant
Steepness
Break point
Dependent
Variable
Decline
Formula
Proportions
Initial Value
Independent
Variable
Gradual
Tilt
Downgrade
Upgrade
Gradient
Angle of
ascent
Angle of
descent
Incline
Substitution
Elimination
solution
System
Infinite

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Solving and interpreting a system of linear equations by graphing

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Interpreting solutions of systems of linear equations

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Analyzing special types of linear systems

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Solutions of systems of equations

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Verify whether a given pair of values is a solution to a system of equations.

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Solving systems of equations with elimination

Solving systems of equations with elimination

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Systems of equations with elimination challenge (practice) | Khan Academy

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Substitution Method

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Solving systems of equations with substitution

Solving systems of equations with substitution

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Systems of equations with substitution (practice) | Khan Academy

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Graphing Method

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Systems of equations with elimination: King's cupcakes

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Sal uses simple elimination to figure out how many cupcakes are eaten by children and adults.

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Systems of equations with elimination: potato chips

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Sal solves another system of equations using elimination.

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Solutions to systems of equations- Intro (possibly use on pear deck)

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Systems of equations with substitution: potato chips

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To solve a system of equations using substitution... 1. Isolate one of the variables in one of the equations, e.g. rewrite 2x+y=3 as y=3-2x. 2. You can now express the isolated variable using the other one. *Substitute* that expression into the second equation, e.g. rewrite x+2y=5 as x+2(3-2x)=5. 3.

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Solving Systems using Substitution (notes)

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Solving systems by substitution powerpoint

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Math08 Unit 3 Final Review

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Math08 Unit3 Final Exam Review- student copy