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Determining Number of Solutions for Linear Equations

Algebra 1: Master Core Concepts & Problem Solving

Numbers

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Squares and Square Roots

Square Root of a Perfect Square

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Cubic and cube roots

Cube root of a perfect cube

Ratios and Proportions

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Ratios

Ratios - Find The Missing Value LHS

Ratios - Find The Missing Value RHS

Equivalent Ratios

Rates

Find the Biggest Rate 

Find the Unit Price 

Unit Rate Fill in Box

Find the Quickest Rate 

Unit Rate

Proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

Percents

Percents, fractions, and decimals

Conversion — Decimal to Fraction

Conversion — Decimal to Percent

Conversion — Fraction to Decimal

Conversion — Fraction to Percent

Conversion — Percent to Decimal

Conversion — Percent to Fraction

Percents – Word Problem

Convert a Decimal to a Fraction

Convert a Decimal to a Percent

Convert a Fraction to a Decimal

Convert a Fraction to a Percent

Convert a Percent  to a Decimal

Convert a Percent to a Fraction

Percents Fractions And Decimals – Word Problem

Measurement

Conversions between metric and imperial systems

Metric to Imperial Conversions

Imperial to Metric Conversions

Conversions Between Metric and Imperial Systems Speed KM to MI

Conversions Between Metric and Imperial Systems Speed  MI to M

Metric-Imperial Length Conversion Inch To Cm

Metric-Imperial Length Conversion MM/CM/M/KM To FT

Metric-Imperial Length Conversion MM/CM/M/KM To MI

Metric systems

Add and Subtract Mixed Units

Metric Length Conversion

Add or Subtract Different Metric Units Convert to CM

Add or Subtract Different Metric Units Convert to M

Add or Subtract Different Metric Units Convert to MM

Imperial systems

Imperial Length Conversion

Scale diagrams

Similar triangles

Pythagorean theorem

Pythagorean Theorem

Applications of pythagorean theorem

Introduction to volume

Calculate the Volume

Surface area and volume of prisms

Coordinate Graphs

Distance formula: d = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Solve Equations

Introduction to linear equations

Applications of linear equations

Absolute Value Equations and Inequalities

Solving absolute value equations

Solving absolute value inequalities

Solving Absolute Value Inequalities Involving "less than"

Solving Absolute Value Inequalities Involving "greater than"

Recognizing Absolute Value Inequalities with "No Solution" or "All Real Numbers"

Data and Graphs

Reading and drawing bar graphs

read and draw bar graphs

Reading Bar Graphs

Reading and drawing histograms

Reading and drawing line graphs

Reading Line Graphs

Box-and-whisker plots and scatter plots

Reading and drawing Venn diagrams

Stem-and-leaf plots

Stem and leaf plots

The Leaf and Stem of Numbers

Recognizing the Leaf and Stem of Numbers

Recognizing The Leaf And Stem of Numbers Leaf

Recognizing The Leaf And Stem of Numbers Stem

Reading Stem and Leaf Plots — Median

Reading Stem and Leaf Plots — Range

stem and leaf plots Range

Reading Stem and Leaf Plots

Reading Stem and Leaf Plots — Mean

Reading Stem and Leaf Plots — Mode

Number Sequences

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Geometric sequences

Sigma notation

Relations and Functions

Understand relations between x- and y-intercepts

Identifying functions

Function notations

Function notation

Set Theory

Set notation

Understanding How to Use Set Notation

Set builder notation

Intersection and union of 2 sets

Intersection and Union of 2 Sets

Intersection and union of 3 sets

Intersection and Union of 3 Sets

Direct and Inverse Variation

Direct variation

Identifying direct variations

Relationship between two quantities

Understanding graphs of linear relationships

Linear relations

Linear Functions

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Slope-Y-intercept form: y = mx + b

Slope intercept form: y = mx + b

General form: Ax + By + C = 0

Point-slope form: \(y - y_1 = m (x - x_1)\)

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

Parallel line equation

Perpendicular line equation

Applications of linear relations

Linear Inequalities

Express linear inequalities graphically and algebraically

Graph the Inequality

Linear Inequalities – Word Problem 

Linear inequalities

Solving one-step linear inequalities

One-step Linear Inequalities

One-step linear inequalities

One-step Linear Inequalities Decimal

One-step Linear Inequalities Decimal with Fraction

One-step Linear Inequalities Fraction

Solve One Step Linear Inequalities Find Solution– Word Problem

One-step Linear Inequalities — Word Problem

Systems of Linear Equations

Money related questions in linear equations

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Using elimination method to solve systems of equations

Solving systems of linear equations by elimination

Using substitution method to solve systems of equations

Solving systems of linear equations by substitution

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Algebra 1

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Mastering the Art of Determining Solutions in Linear Equations

What You'll Learn

Identify whether a system of linear equations has one, no, or infinite solutions

Recognize that different slopes produce one solution where lines intersect

Understand that identical slopes with different y-intercepts create parallel lines with no solution

Determine that identical equations produce infinite solutions as lines overlap completely

Convert linear equations to slope-intercept form to compare slopes and intercepts

What You'll Practice

Analyzing systems to determine the number of solutions by comparing slopes

Converting equations from general form to slope-intercept form

Finding values of constants that produce one solution or no solution

Classifying systems as one solution, no solution, or infinite solutions

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

3 Video lessons

Learning resources

Skills

Systems of Equations

Linear Equations

Slope-Intercept Form

Parallel Lines

Number of Solutions

Graphing