SOLUTION: Consider the system of equations: x + ay = 4 ax + 9y = b (A) For which value of a does

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Consider the system of equations: x + ay = 4 ax + 9y = b (A) For which value of a does       Log On


   

Question 976020: Consider the system of equations:

x + ay = 4
ax + 9y = b
(A) For which value of a does the above system of equation have a unique solution?
(B) Find the values of a and b for which the system has MORE THAN ONE set of solutions.

Please help me, I have tried everything. Please show the steps for the answer as well. Thank you
Answer by josgarithmetic(39627) About Me  (Show Source):
You can put this solution on YOUR website!
system%28x+%2B+ay+=+4%2C+ax+%2B+9y+=+b%29

Their corresponding slopes are system%28-1%2Fa%2C-a%2F9%29.


UNIQUE SOLUTION?
The slopes must be not equal.
-1%2Fa%3C%3E-a%2F9
-9%3C%3Ea
-
a can be ANY real number NOT equal to -9, and the system will have ONE solution; but realize, another requirement is b%3C%3E4.

MORE THAN ONE SOLUTION?
Values for a are ANY real number a%3C%3E-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.