Answer: 0
There are no solutions to this system.
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Explanation:
Let's simplify and rearrange terms for the first equation. The goal is to get it into the form Am+Bn = C, where A,B,C are constants.
4(m-n) = 7(1-n)
4m-4n = 7-7n
4m-4n+7n = 7
4m+3n = 7
Let's do the same for the second equation
(3/2)n = 4 - 2m
3n = 2(4-2m)
3n = 8 - 4m
4m+3n = 8
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The result of each simplification is that we ended up with 4m+3n on the left hand side for each equation. The only difference is that we got 7 for the first equation and 8 for the next one.
This is a contradiction because 4m+3n can only equal one number at a time for any given (m,n) pair. It's like saying z = 7 and z = 8 at the same time, where z = 4m+3n. But z can only equal one value at a time.
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In summary, the given system leads to a contradiction and the system is inconsistent. This means that there are no solutions. There are 0 ordered pairs (m,n) that make both original equations to be true.
