How many solutions does the system of equations have?
6x+y=2
-18x+3y=12

There will be one solution. To solve that:
1. Get the y alone by switching the places.
6x+y=2 > y=2-6x 
-18x+3y=12 > 3y=12-18x > Then divide 3 on each number > y=4-6x
After doing that, you can solve this in graphing or algebra way.

Ima do the algebra way: 

SO we have 2 system of equations. Now pick one equestion.
I will pick, y=2-6x. Now Ima replace the Y with the other equation y=4-6x >  
4-6x=2-6x.

Now solve. And get >  0 aka Infinite Solution.

See if they are paralell, if they are, there are no solutions
thn see if they are the same line, if they are, there is infinite soutions

so

6x+1y=2
-18x+3y=12
divide 2nd equation by -3
6x-y=4

compare
6x+y=2 and
6x-y=4
they are actually perpenduclar
mean 1 soltuions

if yo wantedsoltion
add

6x+y=2
6x-y=4 +
12x+0y=6
12x=6
x=1/2

6x+y=2
6(1/2)+y=2
3+y=2
y=-1

x=1/2
y=-1
(1/2,-1)
1 soluiton