Question 976020
{{{system(x + ay = 4, ax + 9y = b)}}}


Their corresponding slopes are  {{{system(-1/a,-a/9)}}}.



UNIQUE SOLUTION?
The slopes must be not equal.
{{{-1/a<>-a/9}}}
{{{-9<>a}}}
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a can be ANY real number NOT equal to {{{-9}}}, and the system will have ONE solution; but realize, another requirement is {{{b<>4}}}.


MORE THAN ONE SOLUTION?
Values for a are ANY real number {{{a<>-9}}}  AND {{{b=4}}}.  This is that the two equations must be equivalent; they may look different but must satisfy the same line, have the same graph.