If a linear system has four equations and seven variables, then it must have infinitely many solutions. this statement is false, could you explain why and give an example?

False. See the explanation below.

Step-by-step explanation:

We need to proof if the following statement "If a linear system has four equations and seven variables, then it must have infinitely many solutions." is false.

And the best way to proof that is false is with a counterexample.

Let's assume that we have seven random variables given by and we have the following four equations given by the following system:

  (1)

   (2)

  (3)

  (4)

As we can see we have system and is inconsistent since equation (1) is not satisfied by equation (2) ,(3) and (4) if we add those equations we got:

So then we can have a system of 7 variables and 4 equations inconsistent and with not infinitely solutions for this reason the statement is false.

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

this can also be written as

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.