How many solutions the system has? Please help

Question

How many solutions the system has?

7x-6 = y

7/y - 1/x = 12/xy

A- One solution since the second equation can be written as a linear equation that has a different slope from the first equation.

B- Infinitely many solutions.

C- One solution since the graph of a linear equation must intersect the graph of a non-linear equation at exactly one point.

D- No solutions since the second equation is not a linear equation.

E- No solutions since the second equation can be written as a linear equation that is parallel to but does not overlap with the first equation.

Thank you for your help :)

Answer 1

The answer would be (E) since the first the first equation is

7x - y = 6

and second equation after some manipulation

7x-y = 12

which makes it parallel to the first line

Answer 2

First, simplify the second equation.

7/y - 1/x = 12/xy

(7x)/(xy) - (y)/(xy) = (12)/(xy)

7x - y = 12 or y = 7x - 12

Looking at the first equation we have 7x - 6 = y

or

7x - y = 6

If you put the coefficients into matrices, it's simple to see that there is no solution. However, I'm not sure if you've done matrices to let's use substitution:

y = 7x -12

y = 7x - 6

Substituting for y we get

7x - 6 = 7x -12

7x - 7x = 6

0 = 6

No solutions.

Answer 3

7/y - 1/x = 12/xy multiply all 3 terms by xy to eliminate fractions

7x -y = 12 solve for y

y= 7x-12 compare to y=7x-6

E is the correct answer. 7 is the common slope so the lines are parallel

parallel lines do not intersect. there is no solution