I have a problem that is supposed to be solved with the elimination method, but I think this problem is unsolvable

Question

my problem is 

 

9x-3y=6

6x-2y=14

 

This is how I tried to solve the problem:

(2)9x-3y=6(2)

(-3)6x-2y=14(-3)

 

 18x- 6y=12

-18x+6y=-42

 

no matter how I try to solve this problem with elimination it eliminates both x and y.

am I missing something or is this problem unsolvable?

Answer 1

Given:

   9x-3y=6
   6x-2y=14

you may reduce them to be:

   3x - y = 3                    [divide by 3]

   3x - y = 7                    [divide by 2]

 

Now, you either convert these into slope-intercept form or else you convert Ax+By=C into slope intercept form and you find that the slope, m=(-A/B), is the same for the two lines [note: m=3].

 

Two lines with the same slope are parallel.  What does that say about a solution (that is, their intersection)?  What is the term for two lines that are parallel and thus have no solution?

Answer 2

9x - 3y = 6

6x - 2y = 14

 

Look what happens when the 2nd 

equation is multiplied by (3/2)

 

9x - 3y = 6

9x - 3y = 21

 

Both lines have slope m=3

These are parallel lines with different

y-intercepts.  There is no common 

point where they cross.  The solution

is the empty set.

Answer 3

You're not missing anything, Tina. If you use the Elimination Method, you wind up with a mathematical statement saying that:

 

0 = -30

 

Of course, this is false. Therefore, the system has no solution. This does happen sometimes.