4. [3 marks] Solve the system of linear equations if it is consistent, or prove that there is no solution if the system is inconsistent: 2y + z 4x 5z 10x + 4y + 8z x = = = 2 1 4…
3. Consider the following system of equations with unknowns x1 , x2 and x3 :…
The terms point, line, and plane are referred to as undefined. When you write the definition of these terms, you have to rely on other terms that need defining.…
In these problems, we had to identify variables, constraints, and make equations that expressed them. In most cases, the variables represent a value for a certain item, for example in the unit problem, the variable, p, could represent the number of dozens of…
In the last activity, we talked about how situations, rules, x-y tables, and graphs all relate to each other and connect. Now, we’ll look at how situations, rules, x-y tables, and graphs relate and connect to linear functions.…
This course introduces basic algebra concepts and assists in building skills for performing specific mathematical operations and problem solving. Students will solve equations, evaluate algebraic expressions, solve and graph linear equations and linear inequalities, graph lines, and solve systems of linear equations and linear inequalities. These concepts and skills will serve as a foundation for subsequent business coursework. Applications to real-world problems are also explored throughout the course. This course is the first half of the college algebra sequence, which is completed in MAT 117, Algebra 1B.…
Pick one of the following problems. Show how you would solve it using a system…
6- A non-unique solution to a linear program indicates the existence of more than one optimal point with different values of the decision variables but the same value of the objective function.…
To solve a system of equations by addition or subtraction (or elimination), you must eliminate one of the variables so that you could solve for one of the variables. First, in this equation, you must look for a way to eliminate a variable (line the equations up vertically and look to see if there are any numbers that are equal to each other). If there is lets say a –2y on the top equation and a –2y on the bottom equation you could subtract them and they would eliminate themselves by equaling zero. However, this equation does not have any equal terms. So instead we will multiply one or both equations by a number so that they will equal each other resulting in elimination. In this equation we will want to manipulate both equations so that the y’s will both equal –6 (I chose –6 because it is a common term among –2 and –3). Multiply the WHOLE top equation by 3 to equal –6y (you have to multiply 7, -2, and 4 by 3. The outcome of the other two numbers will not matter to the overall equation.) Then multiply the bottom by 2 to equal –6 as well. Again, you have to multiply 2 to the WHOLE equation. Once you finish manipulating the equations you can now eliminate the y variable and only solve for x. If you subtract the -6y’s you must subtract the other numbers from each other as well. After you solve for x, plug it in to any one equation and then solve for…
In linear programming, if there are three constraints, each representing a resource that can be used up, the optimal solution must use up all of each of the three resources.…
Algebra has long been taught in the same way. This usually means teachers rely heavily on the textbook. Though some textbooks have changed in recent years, the central focus is till on paper and pencil, memorization of rules, and use of algorithms. The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) asks mathematics teachers to seek activities that “model real-world phenomena with a variety of function” and “represent and analyze relationships using tables, verbal rules, equations, and graphs”. The standards also urge teachers to give students the opportunity to be actively involved in math through data analysis and statistics that are integrated into the curriculum. My hope is to show that these types of activities can be incorporated into an algebra I course as a way of teaching slope, y-intercept, and linear equations.…
2. In the coordinate system of graphs, there are two main relationships between two variables. With the use of numerical examples, describe these two relationships.…
a. Explain exactly what is meant by multicollinearity in this model. Extreme multicollinearity means that one of the RHS variables is perfectly linearly related to the remaining…
Algebra, some of us fear it while some of us embrace it, algebra is not “arithmetic with letters” it is better described as a way of thinking. At its most fundamental level, arithmetic and algebra are two different forms of thinking about numerical issues. Many of these examples have been taken from our classroom discussions while others are examples I have discovered in my own research for this paper, several examples of each will be cited.…