Question

determine which of the following represents a system of linear equations.
i
( d = 3.9c )
( d = 5c - 2 )
ii
( -9c - 7d )
iii
( 5.1c = 2.91 - 3.43d )
( d = 5c - 2 )
iv
( c = 8 )
( d = 8 - c )

Explanation:

Step1: Define linear system criteria

A system of linear equations consists of two or more linear equations (variables have degree 1, no products of variables) with the same set of variables.

Step2: Analyze Set I

Both equations $d=3.9c$ and $d=5c-2$ are linear (variables have degree 1), share variables $c,d$.

Step3: Analyze Set II

Only one equation $-9c-7d$ (not even an equality), so not a system.

Step4: Analyze Set III

Equation $5.1c=2.91-3.43d$ is linear, but only one equation, so not a system.

Step5: Analyze Set IV

Both equations $c=8$ and $d=8-c$ are linear, share variables $c,d$.

Answer:

I ($d=3.9c$; $d=5c-2$) and IV ($c=8$; $d=8-c$) are systems of linear equations.