SOLUTION: Is the system 6x+7y=63 and y= -3/7x + 6 inconsistent? THANK YOU FOR TAKING YOUR TIME TO HELP ME!!! GREATLY APPRECIATED!!

Question 1105463: Is the system
6x+7y=63 and y= -3/7x + 6 inconsistent?
THANK YOU FOR TAKING YOUR TIME TO HELP ME!!! GREATLY APPRECIATED!!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Solve the first equation for y
6x+7y=63
6x+7y-6x=63-6x
7y = -6x+63
7y/7 = (-6x+63)/7
y = (-6/7)x + 63/7
y = (-6/7)x + 9
This equation is in the form y = mx+b where the slope is m = -6/7

The second equation y = (-3/7)x+6 is in the form y = mx+b where the slope is m = -3/7

Because the two slopes (-6/7 and -3/7) are different, this means that the lines are not parallel. Parallel lines only happen if the slopes are the same with different y intercepts.

The non-parallel lines intersect at exactly one point. So this system is consistent. A consistent system has at least one solution.

So to answer your question, no this system is not inconsistent. The lines would need to be parallel for an inconsistent system.

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