SOLUTION: 2x − y = 5 4x − 2y = t (a) Determine a particular value of t so that the system is consistent. (b) Determine a particular value of t so that the system is inconsiste

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Question 1030241: 2x − y = 5
4x − 2y = t
(a) Determine a particular value of t so that the system is consistent.
(b) Determine a particular value of t so that the system is inconsistent.
(c) How many different values of t can be selected in part (b)?
Answer by ikleyn(52800)   (Show Source): You can put this solution on YOUR website!
.
2x − y = 5
4x − 2y = t
(a) Determine a particular value of t so that the system is consistent.
(b) Determine a particular value of t so that the system is inconsistent.
(c) How many different values of t can be selected in part (b)?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Notice that the left side of the second equation is doubled left side of the first equation.

Therefore, the system of the two equations is consistent if and only if the right side of the second equation is doubled right side 
of the first equation.

So, the answers to questions are:

(a) Determine a particular value of t so that the system is consistent.     Answer.  t = 10.

(b) Determine a particular value of t so that the system is inconsistent.   Answer.  All values (each value) of t =/= 10. 
                                                                                     For example, t = 11.

(c) How many different values of t can be selected in part (b)?             Answer.  Infinitely many.


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