How many solutions does the system of equations have?
y - 7x = -14 and 7y - 49x = -2

one
two
infinite
no solution

Question

How many solutions does the system of equations have?
y - 7x = -14 and 7y - 49x = -2

one
two
infinite
no solution

luigi0210 · Answer

Let's get them into slope-intercept form.

anonymous · Answer

okay I know how to do that

luigi0210 · Answer

Okay, so put each in $$\LARGE y=mx+b$$ and show me what you get.

anonymous · Answer

the slope intercept form of 7y - 49x = -2 is y = 7x - 2/7

luigi0210 · Answer

Yea, now what about the first equation?

anonymous · Answer

y = 7x - 14

luigi0210 · Answer

Correct, so now we have:
$$\LARGE y=7x-14$$and $$\LARGE y=7x-\frac{2}{7}$$
Notice anything about them> Anything they have in common?

anonymous · Answer

the slope is the same

anonymous · Answer

If they have the same slope but different y-intercepts, there is no solution correct?

luigi0210 · Answer

Exactly! And now that we have this information, we are left with deciding whether they have no solution or infinitely many. 
And yea, that's right :)
They are parallel, so they never cross. Nice job :)

anonymous · Answer

Thank you! (: I have a hard time remembering these rules, is there a key or chart of some sort?

luigi0210 · Answer

Hmm, I don't have much.. just this:

luigi0210 · Answer

But the key would be looking at the equations.

anonymous · Answer

Okay! thanks so much! (:

luigi0210 · Answer

Anytime, and welcome to the site ^_^