How many positive integral solutions are possible for the equation?
Solution: Total number of factors of 121 is 3. Case 3: N is an even number and not a perfect square. Example: How many positive integral solutions are possible for the equation X2– Y2= 160? So, total number of positive integral solutions = 8/2 = 4.
How many solutions does ax by C have?
The linear equation ax + by + c = 0 can have only two solutions.
What is C in AX by C?
Alan P. Jun 1, 2015. Ax+By+C is a generalized form (in fact the standard generalized form) for a linear equation. where A,B,andC are placeholders for constants (the x and y are variables).
How do you find the number of non-negative solutions of ax+by=C?
Note: In equation Ax + By = C, if C is divisible by any of A or B, then number of non-negative integral solutions = {C/LCM (A,B)} + 1 Case-1: Positive integral solutions. Let us understand the concept from an example: X 1 + X 2 + X 3 = 8.
How many positive integral solutions are possible for the equation 121?
Solution: Total number of factors of 121 is 3. Case 3: N is an even number and not a perfect square. In this case, total number of positive integral solutions will be = [Total number of factors of (N/4)] / 2 Example: How many positive integral solutions are possible for the equation X 2 – Y 2 = 160?
How do you find the first integral solution of an equation?
(Number of Integral Solutions) Step-2: For a given equation, you should start substituting values (by hit and trial) for the variable that has larger coefficient to find out first integral solution. In this case, it is y. Now, if we take y = 0, we will get x = 39/2 (not an integer). Again, if we take y=1, we will get x = 18.
How many non-negative integral values can X take?
As lowest non negative integral value of y is 1,highest allowable positive value of x is 18 and it is decreasing by 3. So, x can take 7 non negative integral values and they are- 18, 15, 12, 9, 6, 3 and 0.Hence the given equation has 7 non negative integral values.