### Systems of Two Linear Equations in Two Variables Video 1

Explaining the format and possible solutions for a system of two linear equations

This video explains how to solve the following system of linear equations using algebraic substitution. You can try to find the domain before watching the video and click "Reveal Answer" to see if you are correct.

**Problem:** Solve the following system of linear equations: \begin{align*} x+y&=2\\

-2x+y&=-1\end{align*}

Reveal Answer

\((x,y)=(1,1)\)

Explaining the format and possible solutions for a system of two linear equations

Solving a system of two linear equations with two variables using the elimination method

Solving a system of two linear equations using a TI-84 calculator

Solving a system of two linear equations using a TI-84 calculator

Solving a system of two linear equations using a TI-84 calculator

Explaining the format and possible solutions for a system of two linear equations

Finding the point where two lines in three-dimensional space intersect

Explaining the main three forms for linear equations

Discussing properties of linear functions

Discussing the types of linear graphs including horizontal and vertical lines and their properties

Discussing how to write the equation of a line through two given points

Writing a linear equation of profit from a business word problem

Solving a linear equation algebraically and showing how this relates to the graph

Solving a linear equation algebraically

Solving a linear equation algebraically and showing how this relates to the graph

Writing the equation of a line that passes through two points

Finding the slope of a line through a pair of points

Writing the equation of a line with an undefined slope and a given point

Writing the equation of a line with a zero slope given a point

Finding the x and y-intercepts for a line

Solving for a constant so a line has a particular x-intercept

Graphing a line without using technology

Graphing a line without using technology

Graphing a line without using technology

Determining the change in y as x increases for a line

Determining the change in x as y decreases for a line

Determining the slope of a line given points containing a variable

Writing a function for the value of an item depreciating linearly over time

Finding linear functions for the cost, revenue, and profit of a business

Finding the linear cost function for a company

Finding the linear revenue function for a company

Finding the linear profit function for a company

Finding a linear demand equation

Finding a linear supply function

Finding the change in y as x increases for a given line

Writing a linear function representing the depreciation of a car

Writing the augmented matrix for a system of linear equations

Determining if given values are solutions to a system of linear equations

Solving a system of linear equations without using technology

Finding the solution to a system of linear equations by graphing

Using a TI-84 to solve a system of linear equations in three variables

Using a TI-84 to solve a system of linear equations in three variables

Writing a system of equations for a given word problem

Answering questions about a demand and supply word problem

Graphing the solution set of an inequality with two variables

Graphing the solution set of an inequality with two variables

Graphing the solution set of system of linear inequalities

Finding the piecewise-defined function for a given graph along with its domain and range

Graphing a piecewise function

Explaining the definition of logarithmic scale and double-log plots

Using logarithms to transform a power function into a linear function

Writing a non-linear function to represent the line graphed on a semilog plot

Finding the equation of a line through two points

Finding the equation of a line through two points

Finding the equations of parallel and perpendicular lines

Finding the equation of a parallel line

Solving a linear system of equations using substitution

Solving a linear system of equations using elimination

Solving a linear system of equations

Cartesian equations and parametric equations of curves

Review of vector functions and parametric equations

Review of the limit definition of a derivative and calculating the derivative

Review of the limit definition of a derivative and calculating the derivative

Review of derivatives and tangent lines to functions and vector equations

Review of the limit definition of a derivative and calculating the derivative

Review of derivatives and tangent lines to functions and vector equations

Review of the limit definition of a derivative and calculating the derivative

Derivatives and tangents to curves

Finding the distance between a point and a line using scalar projection

Finding a vector equation for the line through two points

Finding a parallel vector through a point

Finding a line perpendicular to a vector and passing through a point

Find the Cartesian form and sketch the graph for the parametric equation of a line

Finding a vector equation for the line passing through two points

Examples finding a volume using disks, washers, and by slicing

Cartesian equations and parametric equations of curves

Using the limit definition to find derivatives of functions and vector functions

Review of vector functions and parametric equations

Review of the limit definition of a derivative and calculating the derivative

Review of the limit definition of a derivative and calculating the derivative

Review of derivatives and tangent lines to functions and vector equations

Proving limits using the epsilon-delta definition

Using the limit definition to find derivatives of functions and vector functions

Using the limit definition to find derivatives of functions and vector functions

Review of the limit definition of a derivative and calculating the derivative

Review of derivatives and tangent lines to functions and vector equations

Proving facts about differentials including a product rule

Review of the limit definition of a derivative and calculating the derivative

Review of derivatives and tangent lines to functions and vector equations

Examples involving the tangent line to an exponential function and finding the derivative of hyperbolic cosine

What the derivatives of a function tell us about the shape of its graph

Optimizing values in word problems

Examples finding a volume using disks, washers, and by slicing

Finding an equation of the plane containing two given lines in three-dimensional space

Using the method of Lagrange multipliers to find the extreme values of a function subject to a constraint

Evaluating a line integral along a curve in space

Explaining the concepts of existence and uniqueness for solutions of systems of equations

Solving a system of equations with three equations and three variables

Solving a two systems of equations

Using the Gauss-Jordan algorithm to solve a system of equations

Solving a system of equations by row reducing the augmented matrix

Solving a matrix equation using the inverse of the matrix

Finding the domain of a function with a denominator, square root, and logarithm

Finding the domain of a function with a natural logarithm and denominator

Finding the domain of a function with a square root in the denominator

Finding the domain of a function with a root and a logarithm in the denominator

Finding the domain of a logarithmic function

Finding the domain of even and odd roots

Finding the domain of functions with even and odd roots

Finding the domain of several rational functions

Finding the domain of a rational function

Explaining how to find any holes and vertical asymptotes of a rational function

Finding the domain of a rational function using factoring

Explaining domain restrictions for denominators, even roots, and logarithms

Explaining the standard form for a quadratic equation and the possible number of solutions

Solving quadratic equations with the difference of two squares formula

Solving quadratic equations by factoring

Solving a quadratic equation by factoring

Solving a quadratic equation by factoring

Solving quadratic equations with the quadratic formula and discussing the number of possible solutions

Explaining when a quadratic equation does not have a real solution

Explaining the graph and properties for the parent function of quadratics

Discussing properties of quadratic functions including the vertex, domain, range, and end behavior

Explaining the general properties of even and odd root functions

How to rewrite radical terms as power terms

Explaining how to solve radical equations and then solving example problems

Solving equations with even roots and checking the solutions

Solving equations with odd radicals

Solving equations with multiple radicals

Properties of exponents applied to power and exponential expressions

Properties of multiplying and simplifying power and exponential expressions

Properties of exponents applied to power and exponential expressions

Properties of exponential growth and decay functions

Properties of the exponential function with base e

Simplifying power and exponential expressions using properties of exponents

Simplifying power and exponential expressions using properties of exponents

Simplifying power and exponential expressions using properties of exponents

Simplifying an expression with both power and exponential functions using properties of exponents

Explaining how to solve equations with power and exponential terms

Solving equations with exponential terms

Solving equations with base e exponential terms

Explaining the terminology and rules of logarithms

Explaining the basic properties of logarithmic functions

Expanding logarithmic expressions using logarithm rules

Condensing a logarithmic expression into a single logarithm

Explaining how to solve logarithmic equations

Solving logarithmic equations with a single logarithm term

Solving logarithmic equations with multiple logarithm terms

Solving logarithmic equations with multiple logarithm terms on both sides

Discussing parent functions of rational functions and their properties

Finding horizontal asymptotes for rational functions

Explaining how to do polynomial long division

Finding horizontal asymptotes for rational functions

Determining the end behavior and horizontal asymptotes for rational functions

Explaining basic algebraic operations for fractions

How to simplify rational expressions

Adding and subtracting rational expressions by finding a common denominator

Explaining how to multiply and divide rational expressions

Performing algebraic operations with rational expressions and simplifying the answer

Solving equations that contain rational expressions

Solving an equation that contains rational expressions

Solving an equation that contains rational expressions

Solving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix

Solving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix

Solving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix

Solving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix

Solving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix

Solving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix

Solving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix

Solving a system of equation by writing it as a matrix equation and using the matrix inverse

Finding all local extrema and saddle points for a function of two variables

Explaining matrix operations including addition and multiplication

Solving a system of linear equations with three equations and three variables

Determining the solutions of a system of equations depending on the value of the constants

Defining linear independence for a set of vectors

Determining if three vectors are linearly independent