Equations are at the root of data science. It is what turns data into actionable information by developing mathematical expressions that mimic physical systems. There are two primary ways to solve equations. The first method is a numeric...

This step-by-step tutorial demonstrates fmincon solver on a nonlinear optimization problem with one equality and one inequality constraint. Visit http://apmonitor.com/che263/index.php/Main/MatlabOptimization for source code.

When Gauss-Jordan elimination transforms a matrix representing an inconsistent system of linear equations to reduced row-echelon form, a matrix row containing all zero coefficient entries and a non-zero constant entry is produced,...

In this video, you will learn how to solve pairs of linear equations visually by using visual models. The teacher explains how drawings can help in solving equations and demonstrates this through examples.

In this video, students learn how to solve pairs of linear equations by using patterns. They explore the concept of solutions to linear systems and how they can be represented graphically. By analyzing the slopes and y-intercepts of the...

In this video, the teacher explains how to solve a system of linear equations with constraints. They use examples such as determining the weight of a mouse over time and finding the number of different types of questions on a test. The...

In this lesson, students will learn about horizontal translations of linear equations. They will explore the similarities and differences between two functions, F of X and G of X, and understand how the graphs of these functions are...

In this video series I show you how to determine if a relation is a linear relation. A linear relation is a relation where their are variables do not have negative or fractional, or exponents other than one. Variables must not be in the...

👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves...

In this video, we compare the slopes and y-intercepts of different functions to understand how they are alike and different. By examining graphs and tables of values, we observe how the scaling affects the position of the functions in...

Systems of two linear equations in two variables can have a single solution, no solutions, or an infinite number of solutions. This chapter explains why.

This chapter builds on Algebra chapter 57 which explained the concept of dependency. In this chapter, we see that although it can sometimes be difficult to spot when a system of linear equations is dependent, when a dependent system is...

Although Gauss-Jordan Elimination is typically thought of as a purely algebraic process, when viewed geometrically, this process is beautiful and amazing, providing insights into the underlying mechanisms of the matrix transformations...

When solving a system of linear equations with a single solution, we get a unique value for each variable. But how do we recognize when a system of equations has infinitely many solutions or no solutions?

In this video, the teacher explains how to solve pairs of linear equations using algebraic methods, specifically the elimination method. They provide examples and explain how to decide whether to add or subtract the equations based on...

👉Learn how to solve quadratic functions. Quadratic equations are equations whose highest power in the variable(s) is 2. They are of the form y = ax^2 + bx + c. There are various techniques which can be applied in solving quadratic...

Once a system of linear equations has been converted to augmented matrix form, that matrix can then be transformed using elementary row operations into a matrix which represents a simpler system of equations with the same solutions as...

👉 Learn how to solve trigonometric equations by factoring out the GCF. When solving trigonometric equations involving the multiples of the same trigonometric function. It is very useful to collect similar trigonometric functions together...

👉Learn how to solve a system of equations by substitution. To solve a system of equations means to obtain a common values of the variables that makes the each of the equation in the system true. To solve a system of equations by...

👉 Learn how to solve one step linear equations. By one step we mean equations that take one step to solve. The one step is the inverse operation needed to isolate the variable such as addition, subtraction, division and multiplication...

👉Learn how to solve a system of equations by substitution. To solve a system of equations means to obtain a common values of the variables that makes the each of the equation in the system true. To solve a system of equations by...

👉 Learn how to solve a one step equation. An equation is a statement stating that two values are equal. A one step equation is an equation whose solution can be obtained by performing only one step of operation on the equation. To solve...

In this video we are going to discover what simultaneous equations are, and how to solve them. Simultaneous equations are two or more equations with two or more unknowns. They are called simultaneous because they must be solved at the...

👉 Learn how to solve one step linear equations. By one step we mean equations that take one step to solve. The one step is the inverse operation needed to isolate the variable such as addition, subtraction, division and multiplication...