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Linear Algebra

How do you solve linear equations?

1. What is a system of equations? 2. Solve for X and Y in the following problems. Show all your work. a. X + Y= 10 , 3X + Y = 12 b. 2X + 5Y = 19 , 3X + 3Y = 15 c. 4X + Y = 22 , 2X + 3Y = 16 d. 12X + Y = 174 , 8X - 2Y = 36 3. Suppose Bob owns 2,000 shares of Company X and 10,000 shares of Company Y

This is a multi-question problem that involves a) graphing a straight line given two points, b) graphing two straight lines to find the solution, c) finding the x- and y-intercepts given the equation, d) writing the equation of a linear given the slope and a point, e) solving problems that have two variables, f) finding the equation of a line given two points.

1. Find the values of x and y that solve the following system of equation -5x - 7y = 12 9x - 5y = -4 2. The sum of two numbers is 48. One number is 3 times as large as the other. What are the numbers? 3. Find an equation of the line that is parallel to the line y = 2x - 5 and that passes through the point (8,2)

Substitution and elimination methods

Compare the advantages and disadvantages of substitution and elimination methods with the matrix method to solve systems of linear equations and the relationship these have with matrix method solving.


1. Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this. 5x - 2y = -1 x + 4y = 35 2. Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this. -4x + 9y = 20 -2x - 2y = 10

Linear equations and linear systems

1. Find the intercept, then graph in a document. Y = -40 + 5x 2. On February 10th, Oscar rented a Chevy Trailblazer with a full tank of gas and 13,091 miles on the odometer. On February 12th he returned the vehicle with 13,322 on the odometer. The rental agency charged $92.00 and needed 14 gallons of gas to fill the tan

Algebra: Linear Equations

1 The sum of two numbers os 41. One number 3 times as large as the other. What are the numbers? 2 In a family there are two cars. In a given week, the car gets an average of 20 miles per gallon, and the second car gets 25 miles per gallon. The two cars combined drive a total of 1025 miles in that week, for a total gas a tota

Inequality and Linear Equation in One Variable

1. Solve using the five-step problem-solving process. Don't forget to include the fifth check equation step of the problem- solving process in your answer. The difference between two positive integers is 36. One integer is three times as great as the other. Find the integers. 2. Use an inequality and the five step problem-so

55 Problems on Algebraic Equations and Graphs

2. Use the intercepts to graph the equation. X + 3y = 6 then graph 3. Solve. Then graph Y -5 > -14 The solution is {y|y>__} A. -11 -10 -9) -8 -7 B. -11 -10 (-9 -8 -7 C. -11 -10 [-9 -8 -7 D. -11 -10 -9] -8 -7 4. Multiply -5/8 x (-5/8) =__ 5. Determine whether (7,-2)

Three Algebra Word Problems on Simultaneous Linear Equations

1. At Gwen's garage sale, all books were one price, and all magazines were another price. Harriet bought four books and three magazines for $1.45, and June bought two books and five magazines for $1.25. What was the price of a book and what was the price of a magazine? 2. Ziggy's Famous Yogurt blends regular yogurt that is 3%

linear equation and inequalities in one variable

1. 2. 6u+ 3. w + 10>13 4. 3z + 1 < -14 5. -5w-9 6. Customers of a phone company can choose between two service plans for long distance calls. The first plan has a one-time activation fee and charges cents a minute. The second plan has no activation fee and charges cents a minute. After how man

Algebra - Linear Equation for a School Library

Solve the problem 5). A school library has $15,000 to spend on new books among the four categories of biology, chemistry, physics, and mathematics. If the amount spent on biology books is to be the same as the amount spent on chemistry books and if the amount spent on mathematics books is to be the same as the total spent

Essay problem using conic sections and non-linear systems

I'm offering a lot of credits for this assignment because I really need help - and I am asking for more than just solving a problem. So please don't take this assignment if you can't help with everything I need. I have worked on this problem but I'm not certain it is correct (it seemed to easy and I'm not seeing where conic

Graphing linear equations, word problems.

1. Graph this equation. y = 3/2x +1 2. Determine whether each pair of equations represents parallel lines. y = -5/4 +1, y = 5/4x +3 4. Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this. x + 8y = 8 9x - 5y = -5

Systems of Equations and interpretation of graphical data

The bar graph shows the percentage of Americans who used cigarettes, by ethnicity, in 1985 and 2002. For each of the groups shown, cigarette use has been linearly decreasing. Use this information to solve exercise 72. *GRAPH IS IN ATTACHMENT* 72) In this exercise, let x represent the number of years after 1985 and let y r

Mathematics - Algebra - Functions, Equations & Matrices

17) The demand equation for a certain product is modeled by y = 50-√(0.01x+1) where x is the number of units demanded per day and y is the price per unit. a) Present a graph of the function. b) Approximate the demand if the price is $37.55. 18) Consider the function a) Present a graph of f(x) b) Solve f(x) = 0 c)

Solving Systems of Equations - Real World Example

There are many applications used in the area of solving systems of equations. For example, systems of equations can be used to find the optimal number of items to produce to ensure the highest profit of those particular items. Systems of equations can be solved by four methods: graphing, substitution, elimination or with matrice

Linear equations with constants in denominators.

Step by step solutions to review problems. Linear equations with constants in denominators. Solve each equation. 18.) x/5 = x/6 +1 20.) x/5 - ½ = x/6 22.) x/2 = 3x/4 +5 24.) 2x - 2x/7 = x/2 + 17/2 26.) x + ¼ = 1/6 + 2-x/ 3 28.) 5 + x-2/ 3 + x + 3/8 30.) 3x/ 5 - x-3/ 2 = x+2/ 3

Linear Equations in One Variable

Solve and check the following linear equations: 1. 6x -3 = 63 2. 5x - (2x - 10) = 35 3. 3x + 5 = 2x + 13 4. 3x + 14 = 12x - 5 5. 2 (x - 1) + 3 = x - 3 (x + 1) 6. 2 - (7x + 5) = 13 - 3x 7. 5x - (2x + 2) = x + (3x - 5) 8. 45 - [4 - 2y - 4 (y + 7)] = -4 (1 + 3y - [4 - 3 (y + 2) - 2 (2y - 5)]

Matrix Algebra

1. Given the matrices [010] [100] [100] A=[101] B= 010] C=[000] [010] [001] [00-1] Show that A and B commute, B and C commute but A and C do not. 2. Show that the matrix [1 4 0] [2 5 0] [3 6 0] Is not invertible 3. Find the inv

Algebra 3rd Set of Problems

Rossano, I need help with the followig exercises. I already finish all the exercises I just want to make sure they are done correctly. Thanks for your help. Exercises 1,2,3,4 Section 3.2: Exercise 64 Section 3.4: Exercises 80, 82, and 94 Section 7.1: Exercises 22, 24, 36, 38, 42, 56, and 70 Section 7.2: Exercises 8, 12, 16

Graphing and linear equations

Please see attached for the complete details of the given problems: WEEK HOMEWORK Please add explanation and colored fonts on your answers Page 483, #2 Solve by graphing. Indicate whether each system is independent, inconsistent, or dependent. Page 483, #6 Solve by graphing. Indicate whether each system is inde

Apply Separation of Variables to the PDE to get 2 ODE's

I have included a Wave Equation problem with parts a-c, that has variable tension. It involves separation of variables, the Sturm-Liouville system, and an application to the "Rayleigh Quotient" involving the Eigenvalues. I have included notes on the Sturm-Liouville system with examples and properties. Please refer to these notes

Algebra: Solving and graphing systems of equations

I have a few questions I need help with. What are the steps to solving a system of equation by elimination? What are the steps to solving a system of equation by substitution? What are the steps to solving a system of equation by graphing? Once you have graph a system of equation, how do you check your answer? Whe

Systems of Equations

Systems of equations can be solved by graphing or by using substitution or elimination. What are the pros and cons of each method? Which method do you like best? Why? What circumstances would cause you to use a different method? Review examples 2, 3, and 4 in section 8.4 of the text. How does the author determine what the

Questions on Linear Equations with Steps

Please answer all questions by selecting your answer from the choices provided. When responding please, please be sure to note the question number along with your answer. If your answer is not clear it will be counted as being incorrect. See examples below for how to provide your answer Question 45 c Or Question 61 Answer c