SOLUTION: does the system x-y=9 3x=3y+5 have a solution? I couldn't find one. And is it inconsistent? why or why not?

Question 172767: does the system x-y=9
3x=3y+5 have a solution? I couldn't find one. And is it inconsistent? why or why not?

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
is already in standard form, so put your other equation in standard form, => .

Now multiply the first equation by -3 to get .

Now if you add the two equations term by term you get , which, of course, is absurd. This means that there is no solution to this system and the solution sets of ordered pairs for each of the two equations describe a pair of parallel lines in . The lines never intersect, therefore the solution set of the system is the empty set.

Such a situation is defined as an inconsistent system.

Compare the given situation with:

This will reduce to , a true but trivial statement. This is an undetermined system -- graphically two equations for the same line. The solution set for the system has an infinite number of elements, namely the entire set of ordered pairs in the solution set for either of the equations.
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