Exam 4: Systems of Linear Equations and Matrices

Use Gauss-Jordan row reduction to solve the given system of equations. ​ ​ 3x-y-z=4 x+y+z=8

Find the solution to the system of equations. 11x-y =-6 25x-3y =-16

Find all solutions of the given system and choose the graph of the system that shows the solutions. x-y=0 x+y=10

In a certain month, Nortel (NT) stock started and ended the month valued at $4.5 a share, and Altria Group (MO) increased from $42 to $46 a share. If you invested a total of $5,250 in these stocks at the beginning of this month and sold them for $5,690 at the end of this month, how many shares of each stock did you buy __________ shares of NT __________ shares of MO

Use Gauss-Jordan row reduction to solve the system of equations. 6x+y=12 6x+8y=5

Find the solution of the given system. ​ -4x+y =-6 8x-2y =12 ​ If the equations of the system are redundant, or if a system is inconsistent, so indicate.

Use Gauss-Jordan row reduction to solve the given system of equations. x-2y+z-4w=5 x+3y+7z+2w=3 2x+y+8z-2w=8

The U.S. Senate has 100 members. For a bill to pass with a super majority, at least twice as many senators must vote for the bill as against it. If 93 senators vote, how many must vote for a bill for it to pass with a super majority ?

Use Gauss-Jordan row reduction to solve the system. ​ 3x+y-2z= -3 2x-3y+2z= 15 x+y+z= 5

Use the table and the given X-ray absorption diagrams to identify the composition of each of the regions marked by a letter. The number in each region shows its absorption, and the number on each X-ray beam shows the total absorption for that beam. Type Air Water Gray matter Tumor Blood Bone Absorption 0 1,000 1,020 1,030 1,050 2,000 $a = 3070$ , $b = 5100$ , $c = 3060$ , $d = 1050$ x = __________ y = __________ z = __________ u = _________

If adding two linear equations gives $x = 5$ and subtracting them gives $y = 5$ , then the graphs of those equations are:

If the addition or subtraction of two linear equations results in the equation $0 = 3$ , then the graphs of those equations are ______.

Find the solution to the system of equations. 3y-2x =-2 12y-8x =1

If adding two linear equations gives $x = 5$ and subtracting them gives $y = 5$ , then the graphs of those equations are perpendicular.

Big Red Bookstore wants to ship books from its warehouses in Brooklyn and Queens to its stores, one on Long Island and one in Manhattan. Its warehouse in Brooklyn has 700 books and its warehouse in Queens has 2,300. Each store orders 1,500 books. It costs $1 to ship each book from Brooklyn to Manhattan and $2 to ship each book from Queens to Manhattan. It costs $5 to ship each book from Brooklyn to Long Island and $4 to ship each book from Queens to Long Island. If Big Red has a transportation budget of $8,900 and is willing to spend all of it, how many books should Big Red ship from each warehouse to each store in order to fill all the orders

The Tubular Ride Boogie Board Company has manufacturing plants in Tucson, AZ and Toronto, Ontario. You have been given the job of coordinating distribution of the latest model, the Gladiator, to outlets in Honolulu and Venice Beach. The Tucson plant, when operating at full capacity, can manufacture 620 Gladiator boards per week, while the Toronto plant, beset by labor disputes, can produce only 410 boards per week. The outlet in Honolulu orders 460 Gladiator boards per week, while Venice Beach orders 570 boards per week. Transportation costs are as follows: Tucson to Honolulu: $10 per board; Tucson to Venice Beach: $5 per board; Toronto to Honolulu: $20 per board; Toronto to Venice Beach: $10 per board. If Tubular Ride Boogie Board Company has a transportation budget of $10,300 and is willing to assure full capacity production at both plants, how many Gladiator boards should be shipped from each manufacturing plant to each distribution outlet

This exercise is based on the following simplified model of the determination of the money stock. M=C+D C=0.2D R=0.1D H=R+C , where M - money stock C - currency in circulation R - bank reserves D - deposits of the public H - high-powered money If the money stock were $108 billion, what would bank reserves have to be $____________billion

Use the table and the given X-ray absorption diagrams to identify the composition of each of the regions marked by a letter. The number in each region shows its absorption, and the number on each X-ray beam shows the total absorption for that beam. Type Air Water Gray matter Tumor Blood Bone Absorption 0 1,000 1,020 1,030 1,050 2,000 ​ ​ $a = 3100$ , ​ $b = 3070$ ​, $c = 3080$ ​ x = __________ y = __________ z = __________

Use the table and the given X-ray absorption diagrams to identify the composition of each of the regions marked by a letter. The number in each region shows its absorption, and the number on each X-ray beam shows the total absorption for that beam. Type Air Water Gray matter Tumor Blood Bone Absorption 0 1,000 1,020 1,030 1,050 2,000 $a = 3100$ , $b = 3080$ , $c = 3070$

Find all the solutions to the given system, and check your answer graphically. -2x+3y =-1 x-y = If the equations of the system are redundant, or if a system is inconsistent, so indicate.