Question 203219
solve the following system of equations using algebra. state whether the system is consistent/ inconsistent and dependent/independent.
3x-2y=7
4y=6x+10
so, I found points for each equation and graphed them. I found that the two equations are parallel to each other, so the would be inconsistent/independent- there are no solutions
is that right?



You are correct that these equations form parallel lines.  How do I know that without graphing?  Well, I solved for "y" in each equation, so that I could see the equation in a y = mx + b format.  In this format, I can easily see the slope (which is the 'm' in the equation) and in each case, the slope was 3/2.  


When slopes are equal, the lines are parallel. 


When you have parallel lines, the system is INCONSISTENT (so you were correct) because there is NO SOLUTION (you were correct again!) :-)   And yes, since the equations are not equivalent, they are INDEPENDENT.  So you were correct on all 3 counts.


Now my question to you is:  You said you solved this by graphing both lines.  The directions, however, wanted you to solve this system algebraically.  Do you know how to do that?   If not, re-post and I'm sure someone will show you how to solve a system without having to find points on each equation and graphing.  


However.... you did get a correct answer by your method so good for you! :-)


I hope this helps. :-)