How many solutions does the system of equations have?

3x=-12y+15 and x + 4y=5

Y=6x+2 and 3y-18x=12

x-2y=6 and 3x – 6y =18

y-5x=-6 and 3y-15x=-12

Ok, so I’m having problems with these, so if Steve or Reiny could help with these problems and show the work for them that would help me study that would be great, however I need this done in 20 min. ( I know it’s bad having time limits) but unfortunately I need it done soon… so if you can help, awesome.

3 answers

3x=-12y+15 and x + 4y=5
These two equations are the same. There is a y for any x.

Y=6x+2 and 3y-18x=12
3y = 18 x + 12 is y = 6 x + 4
These are parallel lines that never intersect, no solution

x-2y=6 and 3x – 6y =18
again divide equation 2 by 3 and get
x - 2 y - 6
the two equations are the same, infinite solutions again

y-5x=-6 and 3y-15x=-12
divide second one by 3 and get
y - 5 x = -4
Again two parallel lines never cross, no solutions

Thank you Damon~!

Were they right?