Consider a system of 2 linear equations in 3 variables.Which of the following statements is possible?Select one:The solution set of the system forms a line.The system has 2 solutions.The system has 1 (unique) solution.The system has 3 solutions

Given, We have a 2 linear equations in 3 variables Now, we have to find the possible solution

Answered: Consider a system of 2 linear equations…

Math

Algebra

Consider a system of 2 linear equations in 3 variables. Which of the following statements is possible?

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter11: Matrices And Determinants

Section11.1: Matrices And Systems Of Linear Equations

Problem 1E: If a system of linear equations has infinitely many solutions, then the system is called _______. If...

See similar textbooks

Related questions

Q: Assuming that 1 + 2 + · · · + n = an2 + bn + c, find a, b, and c by substituting three values for n…

Q: Solve the following systems of linear equations:

Q: A system with parallel lines has an infinite number of solutions. O True O False

A: Two parallel line never intersect each other.

Q: The linear quadratic system: y = x² - 3x - 4 and y = x - 8 has how many solution sets? That is, how…

Q: Solve the given system of linear equations using the Gauss- Jordan Elimination. 4.) 2x1 + 7x2 +…

Q: Ax) = 3x + 2 g(x)%3D|x-1|+1

Q: Solve the following system of equations by utilizing elimination. 2х + Зу %3D 23 2х- бу 3-40 ([?], […

A: x , y = ?

Q: Find all solutions to the following linear system by the method of elimination: 4x + 3 y =−4 2x − y…

Q: Find two numbers a and o such that the following system of linear equations is inconsistent. ax- 5y…

A: A system is said to be inconsistent if no solution exist. For a1x+b1y=c1, a2x+b2y=c2, if…

Q: Solve the given system of linear equations using the Gauss- Jordan Elimination. 2.) 2x1 - 2x2 + x3…

Q: . For a system of two linear equations in two variables,(a) How many solutions are possible?(b) What…

A: (a). Three possible solutions to a linear system in two variables :…

Q: If two linear equations have the same graph, then the associated system has infinitely many…

A: In this question we have to find the solution for two equations having same graph

Q: Consider the linear system 4x1 − 7x2 = −33 −3x1 + 8x2 = 44 −3x1 + 7x2 = 37 Note that there are three…

Q: Determine the value of b that would guarantee that the below linear system is consistent. x1 - 3x2 –…

Q: Set up a system of linear equations to represent the network shown in Figure. Then solve the system.

Q: Find the general and a particular solution of the system of linear equatic X1 +2x2-X3 + 3x4 2x, +…

Q: What will the value of k be that would make this linear system is consistent? x1 − 4x2 − 6x3 = -4…

A: To find The value of k is the given linear system is consistent. x1-4x2-6x3=-4 5x1-6x2-5x3=-8…

Q: Mark the following statement true or false: Every system of linear equations has a solution

A: The given statement is false. Let's take a counterexample. x+2y=3 …(1)2x+4y=12 …(2) From the…

Q: If (a, b, c, d) is a solution to a linear system, then the equations of the linear system have at…

A: (a,b,c,d ) is a solution to a linear system, Then (a,b,c,d) ∈ R4

Q: 2x, - x, + 3x, = 24 2x2 - x, = 14 7x, - 5x2

A: According to Gauss-Jordan Elimination method first we will write the given system into augmented…

Q: Solve the system, or show that it has no solution. If the system has infinitely many solutions,…

A: Given: 2x-6y = 10-3x +9y = -15 To solve: The given system of equations.

Q: Solve the following system of Linear equalions 4 %3D -3x, +4x2 -2x3 -3 x, +7x2 -5x, = 6 %3D

Q: Let AX-B be a system of n linear equations in n variables. If IAI 0, there is a unique solution. If…

A: Given that AX=B is a system of n linear equations in n variable.

Q: Solve the following linear system

A: Given, 10-1-2-110-2-1-15x1x2x3=728342

Q: Prove that the system of linear equations Ax = b has a solution if and only if b ∈ R(LA).

A: Let A be an m×n matrix and consider the linear mapping,

Q: Determine whether each of the following statements is true or false, and explain why.;If a system of…

A: Given: If a system of equations has three equations and four unknowns, then it could have a unique…

Q: Refer to the System of Linear Equations below. 4x1 - X2- X3 = 3 -2x1 +6x2 +X3 = 9 -X1 +x2 + 7x3 = -6…

A: Note that you have not indicated what method is to be chosen for iteration, so I am choosing the…

Q: Use A to find the solution to the given system. x +2x, +3x, = 5 2x, +5x, +3x, = 3 %3D +8x, = 17

Q: Determine whether each of the following statements is true or false, and explain why.;When solving a…

Q: If the equations in a system of equations are equivalent, then they are said to be.. inconsistent…

A: Consistent system of equations: A system of equations is said to be consistent if the system have at…

Q: If f a system of tow equations in two variables has infinitely many solutions, then it is…

A: Here we have to determine the true and false statements.

Q: Let's assume that we have the following system of linear equations Ax = b where 3 2 A = 7 -2 -3 2 8.…

A: Given: System of linear equation is given as, Ax=b A=53237-2-328 b=563 The fixed point form of this…

Q: Mark the following statement true or false: If a system of linear equations has more variables than…

A: The given statement is: If a system of linear equations has more variables than equations, then it…

Q: Find all the basic solutions of the given system 2x, + 3x, + x, +4x4 = 6 X, +2x, + 2x3 + 2x, =3

Q: For a system of two linear equations in two variables, (a) How many solutions are possible? (b) What…

A: Given that: System of two linear equations in two variables.

Q: Solve the following system of linear equations by Gaussian Elimination. х, - 3х, + 4х, + 6х, 3D 4…

A: Given set of linear equations isx1-3x2+4x3+6x4=42x1-6x2+3x3+7x4=-2-3x1+9x2-2x3-8x4=8

Q: Solve the given system of linear equations using the Gauss- Jordan Elimination. 3.) 3x1 + 8x2 - x3…

A: The given system of equation is 3x1+8x2-x3=-182x1+x2+5x3=82x1+4x2+2x3=-4 It can be rewritten as…

Q: Given the linear system Ar = b where || 3 -2 A -2 4 -1 and b= 0 1 2 -2

Q: Consider the following system of linear equations.n 1x_1 - 1x_2 + 4x_3 = 4 2x_1 - 1x_2 + 4x_3 = 7…

A: Given: 1x_1 - 1x_2 + 4x_3 = 4 2x_1 - 1x_2 + 4x_3 = 7 0x_1 - 1x_2 + 5x_3 = 1 0x_1 + 0x_2 - 2x_3 = 0

Q: Verify that the following linear system does not have an infinite number of solutions for all…

Q: If a system of linear equations has two different solutions, then it must have infinitely many…

Q: If a system of equations produces 0=0 by the elimination method, it has no solutions. O True O False

A: System of equations have solution of three types 1. One solution If X = a1 and Y = a2 , where a1 and…

Q: solve the following system of linear equation by graphing and identify the type of system.

A: Here, 2 equations are: 2y=-3x+62y=-3x-2

Q: х — 2у + 32 %3D 2 2х — Зу + 82 3 7 Зх — 4у + 132z %3D 8

A: Consider the system

Q: Determine if the following system of linear equations is consistent or inconsistent. Зх +2у-5z %3D 4…

A: Definition - A system of linear equations is called inconsistent if it has no solutions. A system…

Q: How do you determine whether a given ordered triple is a solution of a system of linear equations in…

A: An ordered triple of real numbers that satisfies all equations in the system is known as solution of…

Q: Use the method of Example 8 to find the unique solution to given linear system. 5x1-3x2 -1 6c1 + 2=…

Q: Consider the following system of linear equations 2х, — Зх, + хз — Зх4 + 2x; %3D 6 2x1 – 3x2 + 5x3 –…

A: As per the instruction, we will be answering only the first one. Given: For (1), Here, we need to…

Q: Consider a system of the form a11x1 + a12x2 = 0 a21x1 + a22x2 = 0 where a11, a12, a21, and a22 are…

A: If a system of equation has at least one solution, it is said to be consistent. Given system of…

Question

Consider a system of 2 linear equations in 3 variables.
Which of the following statements is possible?
Select one:
The solution set of the system forms a line.
The system has 2 solutions.
The system has 1 (unique) solution.
The system has 3 solutions

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Systems of Linear Equations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

What is a system of linear equations in the variables x, y, and z?
Using the method of addition, is there only one way to solve the system?
Determine the values of k such that the system of linear equations does not have a unique solution. x+y+kz=3x+ky+z=2kx+y+z=1
If a system of linear equations has infinitely many solutions, then the system is called _______. If a system of linear equations has no solutions, then the system is called ______.