How many solutions are there to the following system of equations?

4x – 14y = 6
–2x + 7y = –3

0
1
2
infinitely many

Question

How many solutions are there to the following system of equations?

4x – 14y = 6
–2x + 7y = –3


       0
       1
       2
       infinitely many

campbell_st · Answer

well take the 2nd equation and multiply it by -2... what do you get..?

anonymous · Answer

How would I multiply it exactly? o.o

campbell_st · Answer

well just double each term and change the sign to the opposite of whats shown

anonymous · Answer

still confuse

anonymous · Answer

-2x*-2=4x
7y*-2=-14y
-3*-2=6
So, the equations are the same. Now, use logic to get your answer.

anonymous · Answer

okay, that makes sense, but can you give me one more step? I'm not quite sure where to take this @curiouscrab

jdoe0001 · Answer

hmm @Levi565   can you solve each for "y"?

jdoe0001 · Answer

what would you get?

anonymous · Answer

How many numbers can you replace x or y with and still have both equations equal? Well since both equations are already equal, then...

anonymous · Answer

Uhhhm.........no they wouldnt be equal

anonymous · Answer

Yes they are. It's very hard to explain.

ranga · Answer

These two equations are essentially the same.  If you multiply the 2nd equation by -2 you get the first equation.  So we have two unknowns: x and y.  But only one equation.  That means you can choose any value for one unknown and use the one equation to solve for the other unknown.  And you can keep doing this forever.  Therefore, this system has ???  solutions.

anonymous · Answer

4x - 14y = 6 (change to slope intercept form )
-14y = -4x + 6
y = -4x/-14 + 6/-14
y = 2/7x - 3/7

-2x + 7y = -3 (change to slope intercept form)
7y = 2x - 3
y = 2/7x - 3/7

since both equations are the same in slope intercept form, then there are INFINITE SOLUTIONS