How to write a system of equations?

Question

Vaughn Bryan · Accepted Answer

Start with:      a    =    2        b    =    3        c    =    -    5  How do we create an equational system where this is the only possible outcome?Option A: Do nothing. This is a set of equations with the desired unique solution. Downside: too obvious.Option B: Since there are       3   unknowns, write       3   linear equations with varying small integer multipliers for the unknowns:      a    +    b    +    c    =    0        a    -    2    b    -    c    =    1        2    a    -    3    b    -    2    c    =    5  This generally works well, except that we can create a set of equations that have multiple solutions. For example, if we chose       3    a    -    3    b    -    c    =    2   for the third equation instead of       2    a    -    3    b    -    2    c    =    5   then there would be an infinite number of solutions.To avoid this, just try solving the question you create.Option C: Go beyond linear. Plenty of scope for imagination here.For example:      3    a    +    2    b    +    c    =    7        3          a      2        +    2          b      2        +          c      2        =    55        3          a      3        +    2          b      3        +          c      3        =    203

osadczyttq · Accepted Answer

I like your answer, really cool

How to write a system of equations?

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