Question 676205
-10x + 2y = 14
-5x + y = 7
these are dependent as can be seen by multiplying the second equation by 2
2(-5x+y=7) to get -10x + 2y = 14
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The lines are the same and every point on the line will be a solution.
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3x+3y=15
x+y=-14
these are not dependent, as they are different lines, multiply the second equation by -3 and add them
3x + 3y = 15
-3(x+y=-14) to get -3x + -3y = 42
3x + -3x + 3y + -3y = 15 + 42
0 = 57
this an untrue statement, so there is no solution for these lines.  
they are inconsistent.
**Notably, these both have the same slope of -1, which means they are parallel and explains why there is no solution.**
{{{graph(300,200,-20,20,-20,20,-x+15,-x-14)}}}
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