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Solving 3 variable systems of equations (no solution, infinite solutions) | StudyPug

College Algebra: Master Core Concepts & Applications

Direct and Inverse Variation

Direct variation

Identifying direct variations

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Inverse variation

Joint and combined variation

Piecewise Functions

Evaluating piecewise functions

Graphing piecewise linear functions

Graphing piecewise non-linear functions

Surface Area and Volume

Surface area of 3-dimensional shapes

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface Area of Prisms Rectangle

Calculate the Surface Area

Surface area of cylinders

Rational Numbers

Comparing and ordering rational numbers

Comparing decimal numbers

Comparing fractions

Solving problems with rational numbers in decimal form

Mixed Operations with Decimals

Mixed Operations

Mixed Operations with Decimals Bracket

Mixed Operations with Bracket Square

Solving problems with rational numbers in fraction form

Operations with fractions

Determine square roots of rational numbers

Square roots of rational numbers

Powers and Exponents

Using exponents to describe numbers

Expanded powers

Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with exponents

Using exponents to solve problems

Number System and Radicals

Understanding the number systems

Prime factorisation

Number properties: Prime or Composite

Number properties: Prime?

Prime factorization

Prime factors – Word Problem

Greatest Common Factors (GCF)

Greatest Common Factor 2 Numbers

Greatest common factors (GCF)

Greatest Common Factor 2 Numbers – Word Problem

Least Common Multiple (LCM)

Least common multiple (LCM)

Lowest Common Multiple - 2 Numbers – Word Problem

Lowest Common Multiple 2 Numbers

Rational vs. Irrational numbers

Converting repeating decimals to fractions

Radicals

Solving radical equations (advanced)

Solving radical equations

Solving Radical Equations Involving One Square Root Term

Solving Radical Equations Involving More than One Square Root Term

Conversion between entire radicals and mixed radicals

Adding and subtracting radicals

Combining Like Radicals

Adding and Subtracting Radicals

Multiplying radicals (advanced)

Multiplying Radicals

Multiplying radicals

Operations with radicals

Operations with Radicals

Evaluating and simplifying radicals

Square and square roots

Square Root of a Perfect Square

Cubic and cube roots

Cube root of a perfect cube

Converting radicals to mixed radicals

Converting radicals to entire radicals

Adding radicals

Subtracting radicals

Multiplying and dividing radicals

Dividing radicals

Rationalize the denominator

Exponents

Product rule of exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

 Power of a power rule

Simplify the power

Power of a power rule

Negative exponent rule

Combining the exponent rules

Scientific notation

Rational exponents

Convert between radicals and rational exponents

Solving for exponents

Factorising Polynomial Expressions

Solving polynomials with the unknown "b" from \(ax^2 + bx + c\)

Solving polynomials with the unknown "b" from ax^2 + bx + c

Factorising polynomials: \(ax^2 + bx + c\)

Factoring polynomials: ax^2 + bx + c

Factoring Polynomials: ax^2 + bx + c

Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Factoring perfect square trinomials

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

Find the difference of squares

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

Evaluating polynomials

Using algebra tiles to factorise polynomials

Solving polynomial equations

Word problems of polynomials

Common factors of polynomials

Factorising polynomials by grouping

Factoring polynomials by grouping

Solving polynomials with unknown coefficients

Solving polynomials with unknown constant terms

Factorising polynomials: x^2 + bx + c

Factoring polynomials: x^2 + bx + c

Applications of polynomials: x^2 + bx + c

Applications of polynomials: x^2 + bx + c

Introduction to Relations and Functions

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Linear Functions

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>

Gradient 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>

Gradient intercept form: y = mx + b

Slope intercept form: y = mx + b

General form: Ax + By + C = 0

Gradient-point form: \(y - y_1 = m (x - x_1)\)

 Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and gradient

Word problems of graphing linear functions

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

Absolute Value Functions

Absolute value functions

Expressing an Absolute Value Linear Function as a Piecewise Function

Expressing an Absolute Value Quadratic Function as a Piecewise Function

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"

Linear Equations

Introduction to linear equations

Introduction to nonlinear equations

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

Parallel line equation

We've got you covered with our complete help for College Algebra, whether it&apos;s for any typical remedial and first year algebra courses in college, <a href="https://clep.collegeboard.org/science-and-mathematics/college-algebra">CLEP</a>, or <a href="http://www.act.org/">ACT</a>.
Our comprehensive lessons on algebra help cover topics including Solving inequalities, Exponents, Matrices, Solving linear equations, Domain and Range, Factoring polynomials, Quadratic equations, Graphing inequalities, just to name a few. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest algebra problems. Then, strengthen your understanding with tons of algebra practice. 
All our lessons are taught by experienced College Algebra teachers. Let&apos;s finish your homework in no time, and ACE that final.

College Algebra

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<h2>What is College Algebra?</h2>
What is Algebra and why do we need it? Algebra can be defined as the branch of math that uses symbols and letters in lieu of numbers to study a variety of phenomena. Often times these symbols represent a simplification of known or unknown variables and factors involved in a complex algebraic equations or formulas. Algebraic equations and formulas are often used to describe a relationship between these variables. The study of Algebra also involves the rules that dictate how these symbols and letters operate.
Understandably, many of you may have thought you escaped Algebra after graduating high school. Kissing polynomials and inequalities goodbye must have left you overjoyed! The reality for many of you however is that Algebra will continue to be fundamental as you begin your college education - In fact, much of Algebra forms the basis of all math you have learnt up to now! The utility of Algebra is particularly prominent in fields of science, technology, engineering and math (STEM). Moving forward and beyond academia, Algebra will continue to be your friend in a process you may know as "growing up". Use StudyPug and gain more than just great grades in this intro to College Algebra! Learn life skills to improve your financial planning and budgeting, assess risks in your business or investment ventures, and make good decisions regarding healthcare insurance.
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<h2>Is College Algebra hard?</h2>
College Algebra will definitely be harder than the likes of <a href="[[region_textbook.html|{"textbook_key":"algebra-1"}]]">Algebra 1</a> or <a href="[[region_textbook.html|{"textbook_key":"algebra-2"}]]">Algebra 2</a>. But if you have completed these courses, you should be well prepared to tackle <a href="[[region_textbook.html|{"textbook_key":"college-algebra"}]]">College Algebra</a>. College Algebra math will build on elementary Algebra concepts you learnt in Algebra 1 and Algebra 2, so not everything will come as a surprise. Furthermore, some of the skills learnt in Algebra 1 and Algebra 2 will be accessed and advanced in College Algebra. Our College Algebra tutors are always available, 24/7 to provide you help with College Algebra. Whether you are just beginning Algebra, or feel like you need to learn Algebra alongside Algebra for dummies, find yourself solving increasingly difficult Algebra problems in no time with the help of our expert, knowledgeable tutors.
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<h2>How to learn College Algebra?</h2>
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<h2>How to pass College Algebra?</h2>
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Solving 3 variable systems of equations (no solution, infinite solutions)

What You'll Learn

Recognize when a 3-variable system has no solution by identifying contradictions

Identify infinite solutions when equations are multiples of each other

Apply elimination methods to pairs of equations in a 3-variable system

Interpret geometric meaning: overlapping planes yield infinite solutions, parallel planes yield none

Verify solution types by analyzing the result after variable elimination

What You'll Practice

Solving systems that result in false statements like 0 = 20

Identifying equations that are multiples of each other

Using multiplication and elimination on equation pairs

Determining whether a system has no solution or infinite solutions

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

3 Video lessons

Practice exercises

Skills

Systems of Equations

Three Variables

Elimination Method

No Solution

Infinite Solutions

Dependent Equations

Inconsistent Systems