Question

I think its no solution. Please help :)

Solve the given system, using the substitution method.

y = 3x – 4
9x – 3y = 14


A.
There is no solution.

B.
(12, 14)

C.
(14, 12)

D.
There are an infinite number of solutions.

Answer 1

There's a variety of ways to substitute, but the first equation already defines y explicitly as a function of x. In other words, y is already by itself.

So, we'll plug it into the second equation:

9x - 3 [ 3x - 4 ] = 14
9x - 9x - 12 = 14
-12 = 14.

Woah, that's not right. -12 is not equal to 14. So, we've reached a false statement. That means that there are no solutions between these two lines.

Answer 2

Oh woops. That should be a +12 instead of a -12. I forgot that the -3 multiplies with the -4 to yield positive 12.

Either way, the solution is still inconsistent since 12 is not equal to 14.