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Systems of EquationsMiss Connell

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Now onto

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Slope of a LineO The slope a of a line through points (x1, y1)

and (x2, y2) is determined by:

O The slope of a horizontal line .

O The slope of a vertical line

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Parallel Lines

Two Parallel lines

have the same

slope

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Perpendicular Lines

Two Perpendicular

lines have slopes

that are negative

reciprocals to oneanother.

The product of

these slopes is -1.

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Equation of a LineO There are various ways ofwriting the equation of a line.Form Equation Role of Parameters Characteristic

Function

or

Standard

Can be used to

describe any

non-vertical line

General Can be used to

describe any line.

Symmetric Can be used to

describe any

oblique line that

does not pass

through the origin.

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Proof Using Analytic GeometryO When proving a geometric statement using

algebra, do the following:

O Represent the figure in a Cartesian plane

O Express the coordinates of the significant points of the

figure using variables taking into account thehypotheses of the statement.

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Graphing

You can graph a linear function using

Table of Values

Function Form

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Let`s Practice

OPage: 94

O 1, 2df, 3ac, 4be, 5, 6, 8, 10, 12

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Systems of EquationsFirst Degree

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Systems of First DegreeEquations

O The solution of systems of equation of the first degree

is the point of intersection for these two lines.

O The Point of Intersection is also described as the

solution set which is an ordered pair: (x, y)

O Systems ofEquations are equivalent if they have thesame solution set.

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Solving a Solution ofEquations

O O

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Table of ValuesO Choose Values forx and calculate values fory.

O The solution exists when both values ofyare

the same

O We can check solution by replacing back into

original equations

O This method can be time consuming and

difficult if the solution is not an integer.

O Other option: graphing on same grid to see

intersection point.

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Table ExampleO

-3

-2

-1

0

-3 1

-2 2

-1 3

0 4

-3 5 1

-2 2 2

-1 -1 3

0 -4 4

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Comparison MethodO

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Comparison ExampleO

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Substitute ExampleO

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Elimination Method1. Create, if necessary, an equivalent system of

equations in which the coefficients of one of the

variables a

re equal o

ropposite

2. Create an equation in one variable by adding orsubtracting the corresponding sides of the equationsof the system. Solve the resulting equation.

3. Substitute the value found in one of the originalequations to determine the value of the othervariable.

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Elimination ExampleO

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Solution to Linear Systems

One Solution

No Solutions

Infinite Solutions

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One SolutionO

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One Solution

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No SolutionsO

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Non-Coinciding

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Infinite SolutionsO

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Coinciding

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PracticeO