Question: Consider the linear equation in three variables x + y + z = 4. Find a pair of linear equations in three variables that, when

Consider the linear equation in three variables x + y + z = 4.

Find a pair of linear equations in three variables that, when considered together with the given equation, form a system having (a) exactly one solution, (b) no solution, (c) infinitely many solutions.

Step by Step Solution

★★★★★

3.34 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Answers may vary Sample answers are given a xyz 4 x2y z 5 2x y 3z 4 This system has e... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related College Algebra Questions!

Consider the linear equation y = b0 + b1x. a. Identify and give the geometric interpretation of b0. b. Identify and give the geometric interpretation of b1.

Use a system of equations to solve the problem. Find an equation of the line y = ax + b that passes through the points (-2, 1) and (-1, -2).

Use a system to find an equation of the parabola through the given points. y (2, 9) (-3, 4) (-2, 1) H

Design and Implement an Algorithm in Java to solve the following problem in solving linear equations using the Gaussian Elimination method. Definition: A system of linear equations can be placed into...

INSTRUCTIONS: 1) Do all necessary steps 2) This is a whole paper. No data is missing. 1. SYSTEMS OF LINEAR EQUATIONS 1.2. Exercises (1) Suppose that In and Ly are lines in the plane, that the...

INSTRUCTIONS: 1) Do all necessary steps 2) This is a whole paper. No data is missing. 1. SYSTEMS OF LINEAR EQUATIONS (8) Consider the following system of linear equations ( where b1, . . ., b are...

2. Shown below are some traffic patterns in the downtown area of a large city. The figures give the number of cars per hour traveling along each road. Any car that drives into an intersection must...

3. Which of the following is the row-reduced echelon form of 4 4 6 8 (a) [6 1 2] () [87 2] () [81 2] ([618] 4. Given the augmented matrix 2 4 2 8 which of the following is not a valid row operation?...

Please provide solutions. Thanks. 1. Which of the following is true about the system of linear equations in two variables? 10. Which of the following equations can be paired with 3x - Zy = 5 to make...

A linear equation in two variables is the equation of a line. A linear equation in three variables gives the equation of a plane. In the case of two linear equations in two variables, you can have: 0...

This is a discrete distribution, with two parameters q and (where 0 q 1, > 0). If a random variable X has a ZIP(q, X) distribution, then its probability mass function px is given by: px (0)...

Show that the magnitude of the magnetic field produced at the center of a rectangular loop of wire of length L and width W, carrying a current i, is 2i (L? + W?)2 B = LW

Why is having sufficient knowledge of the client's business and industry is critical to performing a proper review of the client's statements? Multiple Choice To provide reasonable assurance that the...

25. Suppose the risk-free return is 5% and the market portfolio has an expected return of 15% and a standard deviation of 22%. Johnson & Johnson Corporation stock has a beta of 0.98. What is its...

The area of a rectangle with length 1 and width w is computed by A(1, w) = Iw, and its perimeter is calculated by P(1, w) = 21+ 2w. Assume that I > w and use the method of substitution to solve the...

(a) Find a matrix A and a column matrix B that describe the following tables. (b) Find the matrix product AB, and interpret the result. Student 1 Student 2 Student 3 College A College B College C...

(a) Find a matrix A and a column matrix B that describe the following tables. (b) Find the matrix product AB, and interpret the result. Student 1 Student 2 Student 3 College A College B College A 10...

MACRS depreciation expense and accounting cash flow Pavlovich Instruments, Inc., a maker of precision telescopes, expects to report pretax income of $433,000 this year. The company's financial...

You want to obtain a sample to estimate howr much parents spend on their kids birthday parties. Based on previous study, you believe the population standard deviation is approximately or = 52.1...

Double your wealth. Kant Miss Company is promising its investors that it will double their money every 3 years. What annual rate is Kant Miss promising? Is this investment a good deal? If you invest...