If two systems of linear equations have the same solution set (in other words, the two systems are equivalent), then they must have the same number of equations. a. True
b. False

False.

Step-by-step explanation:

Equivalent systems of equations are those that have the same solutions or roots, although they have different numbers of equations. Equivalent systems of equations must have the same number of unknowns.

In other words, two systems of equations are said to be equivalent when they have the same solutions. Equivalent systems of equations do not have to have the same number of equations, although they do have to have the same number of unknowns.

So, the sentence is false.

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.