## anonymous 5 years ago 6x-5y=35, 5y-6x=-35 what is the solution of the system of the equation, is it a solution and is it consisten or incosistent and is it dependent or independent

1. anonymous

Well, obviously if you add the equations together you zero out...scratching my head....

2. anonymous

I am scratching mines to causes I am not understanding what u saying

3. anonymous

You can see that these two equations are in fact the same equation. Therefore the 'system' is consistent, but is also dependent (the first equation is -1 times the second equation).

4. anonymous

Thank you polpak. I was scrambling for the verbiage.

5. anonymous

Consistent just means that it has at least 1 solution. This one has infinitely many solutions since all the points on the line described by the first equation are also on the line described by the second equation because it's the same line.

6. anonymous

A solution to a system is the set of all the points that every equation in the system has in common.

7. anonymous

So it will be 6x/5 =35 and 5y-6x=-35

8. anonymous

No.. it will be $$y = \frac{6}{5}x - 7$$

9. anonymous

But if its hard to figure out if its a no solution, a point or infinety of many solution and if its consistent or inconsistent , and if its a dependent or independent,

there are infinately many solutions .... and the solution is if y= p (let p be any number) then x= (5*p)/6 + 35/6

11. anonymous

Well both equations yield the same line $$y = \frac{6}{5}x-7$$. So the system has infinitely many solutions because both lines are the same Any point on one is a point on the other. Your system will have infinite solutions when the lines are the same line. Your system will have no solutions when you have lines which are parallel but aren't the same line.(they never cross). Your system will have one solution when they are not parallel (they will cross at exactly one place).

12. anonymous

So therefore it will be consistent and independent

13. anonymous

A consistent and independent system has only one solution. A dependent system has infinite solutions.

14. anonymous

Thanks now I see