Is the given system of equations solvable with back substitution?

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The discussion centers on the solvability of a system of equations with 5 variables and 3 equations. Participants clarify that having fewer equations than variables does not automatically imply no solution. The final row of the augmented matrix suggests a relationship among the variables, specifically 0x1 + 0x2 + 0x3 + 0x4 + 0x5 = 4, indicating that there may be multiple solutions or a unique solution depending on the context. The conclusion is that the system can have either multiple solutions or no solution, depending on the specific equations involved.

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Homework Statement



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Homework Equations





The Attempt at a Solution



I think the answer is no solution because there is 5 variables but only 3 equations. Is that correct?
 

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TyErd said:

Homework Statement



I have attached the question

Homework Equations





The Attempt at a Solution



I think the answer is no solution because there is 5 variables but only 3 equations. Is that correct?

No, that is not the reason. Look at the final row; it is shorthand for an equation involving x1, x2, x3, x4, x5. What is the equation?

RGV
 
do you mean 0x1 + 0x2 + 0x3 + 0x4 + 0x5 = 4?
 
if the third is also an equation that means there must be an answer right? So because we have to assign variables and we have 5unknowns and 3 equations that must mean two values will be variables right?? so the answer has to be B yeah??
 
TyErd said:
do you mean 0x1 + 0x2 + 0x3 + 0x4 + 0x5 = 4?
For what values of the variables x1, x1, x2, x3, and x4 will this be a true statement?


TyErd said:
if the third is also an equation that means there must be an answer right?
Not necessarily. There are three possibilities for a system of equations (which are here represented by an augmented matrix):
1) a unique solution
2) multiple solutions
3) no solution.
TyErd said:
So because we have to assign variables and we have 5unknowns and 3 equations that must mean two values will be variables right?? so the answer has to be B yeah??
 

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