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

3x – 9y = 0
–x + 3y = –3

A.
0

B.
1

C.
infinitely many

D.
2

Question

How many solutions are there to the following system of equations?
 
3x – 9y = 0
–x + 3y = –3
 
 A.
0
 
 B.
1
 
 C.
infinitely many
 
 D.
2

bossimbacon · Answer

@Directrix

bossimbacon · Answer

@DanJS

directrix · Answer

You can write the lines in the y = mx + b format. y = x/3 + 0 and y = x/3 - 1 and observe that the slopes are the same which means that the lines are parallel. The y-intercepts are different so the two lines are distinct. Or, you can observe that the lines are parallel here: http://www.wolframalpha.com/input/?i=3x+%E2%80%93+9y+%3D+0%2C+%E2%80%93x+%2B+3y+%3D+%E2%80%933

directrix · Answer

Of course, the question remains: How many solutions, if any, does the system have?

@Bossimbacon    Post what you think.

bossimbacon · Answer

@midhun.madhu1987

midhun.madhu1987 · Answer

I agree with @Directrix

If 2 lines are parallel, then slopes are equal. Here try to find the slopes of the 2 lines... by converting both equations to the form y=mx+b