[Linear Algebra] - Produce an equation not implied by this system

[Tosh5457]

Homework Statement

I'm quoting the whole exercise:

The Linear Combination Lemma says which equations can be gotten from Gaussian reduction from a given linear system.

Produce an equation not implied by this system:
3x + 4y = 8
2x + y = 3

Homework Equations

Linear Combination Lemma: A linear combination of linear combinations is a linear combination.

The Attempt at a Solution

What does it mean to produce an equation not implied by the system? Is it an equation that can't be derived from the system? In that case, that will be an equation such that it doesn't result from any linear combination of the 2 equations on that system, right?

 

[HallsofIvy]

Homework Statement

I'm quoting the whole exercise:

The Linear Combination Lemma says which equations can be gotten from Gaussian reduction from a given linear system.

Produce an equation not implied by this system:
3x + 4y = 8
2x + y = 3

Homework Equations

Linear Combination Lemma: A linear combination of linear combinations is a linear combination.

The Attempt at a Solution

What does it mean to produce an equation not implied by the system? Is it an equation that can't be derived from the system? In that case, that will be an equation such that it doesn't result from any linear combination of the 2 equations on that system, right?

Yes, that would be my interpretation.