Question

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

Answer 1

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.

Answer 2

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