SOLUTION: Find the value of m that makes y = mx + 3 5x - 2y = 7 an inconsistent system. I have big problems with this. Algebra and me do not get along. Than

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Question 76298This question is from textbook
: Find the value of m that makes y = mx + 3
5x - 2y = 7 an inconsistent system.
I have big problems with this. Algebra and me do not get along. Thanks This question is from textbook

Answer by kev82(151) (Show Source):
You can put this solution on YOUR website!
Hi, An inconsistent system is where there are no solutions at all. Remember that these equations can be drawn as lines. and the solution is where the lines cross. So we need to find a line that doesn't cross the line 5x-2y=7. Does that make sense so far?
Ok, in 2 dimensions,the only situation where lines never cross is if they are parallel. (this isn't strictly true as parallel lines meet at infinity, but forget that). For lines to be parallel they must have the same gradient. The gradient of the second line is clearly m, so all we have to do is find the gradient of the first line and that's your value for m. Still with me?
Ok, so let's rearrange the first line into standard form

so the gradient of this line is 5/2 or 2.5. So m=2.5 is the answer.
Now try solving the equations and check that they are actually inconsistent.
Also not that the parallelness thing only holds in two dimensions as there are many non-parallel lines in 3 dimensions that don't cross. See if you can picture two of them.
Hope that helps,
Kev