SOLUTION: In this systems of equations, how can I figure out what the 2nd equation's minimum/least dollar value is? Purchases of $6 or $4 each month. Is there a better way to solve this?

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Question 1118350: In this systems of equations, how can I figure out what the 2nd equation's minimum/least dollar value is?
Purchases of $6 or $4 each month. Is there a better way to solve this?
Thanks in advance.
m+s=12
6m+4s=?

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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In this systems of equations, how can I figure out what the 2nd equation's minimum/least dollar value is?
Purchases of $6 or $4 each month. Is there a better way to solve this?
Thanks in advance.
m+s=12
6m+4s=?
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The second equation is incomplete; it is only an expression, but not an equation. What are the variables, m and s, supposed to be? quantity counts for $6 and $4 ? If they are, then m%3E=0 and s%3E=0 and each is only whole-numbers or 0.

If vertical axis counts m and horizontal axis counts s then graph for first equation is
graph%28300%2C300%2C-1%2C12%2C-1%2C12%2C12-x%29.
m for vertical axis and s for horizontal axis;
counts y and counts x for m and for x, respectively.

6m%2B4s does not establish any constrain unless it is equated to some value.

Are you trying to make something like f%28m%29=6m%2B4s with m%2Bs=12 as a restriction?
f%28m%29=6m%2B4%2812-m%29
f%28m%29=6m%2B48-4m
f%28m%29=2m%2B48
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df%2Fdm=2, but then this is a constant, and df%2Fdm%3C%3E0.
No minimum for f and no maximum for f.

The SMALLEST value that m can be is 0, and this will make highlight_green%28f%28m%29=f%280%29=2%2A0%2B48=highlight%2848%29%29.