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?
Answer by PRMath(133)   (Show Source):
You can put this solution on YOUR website! 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. :-)
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