Asked by Linden

What value of m makes the following linear system of equations have infinitely many situations.
-6x+5y=14
12x+my=-15

Also, does the value of 3 for m give this system of equations one solution. Lastly, does the value of -10 in this system of equations give no solution?
Answered by Linden
If you can also provide me with the steps for what value of m would give you infinite solutions, that would be great, given that I would like to be able to solve these type of problems on my own.
Answered by oobleck
for infinitely many solutions, the two equations must describe the same line
-6x+5y=14
multiply everything by -2 and you have
12x-10y = -28

The line 12x-10y = -15 provides no solutions, since the two lines are parallel, and do not intersect

setting m=3 makes the two slopes different, so the lines must intersect.
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