Is the given system of equations solvable with back substitution?

[TyErd]

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?

 

[Ray Vickson]

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

 

[TyErd]

do you mean 0x1 + 0x2 + 0x3 + 0x4 + 0x5 = 4?

 

[TyErd]

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??

 

[Mark44]

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?

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.

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??