System of equations with infinite solutions
If the system of equations :
and
has infinitely many solutions then,
Find the value of
The answer is 6.
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1 solution
If there are infinitely many solutions, then there must not be enough information to solve the pair of equations for any specific x and y i.e they must both contain the same information. This happens if one is some multiple, A, of the other;
k x + 3 y − ( k − 3 ) = A [ 1 2 x + k y − k ] = 1 2 A x + A k y − A k .
Now equating coefficients we see that:
3 = A k and k − 3 = A k .
Combining the two we get;
k − 3 = 3 so k = 6 .