2. Find the values and f, for which the following system of the linear equation has an infinite number of solutions. - 2x + 3y = 7E ^ 2 2x + 6 21x = 28
Answers
Answer:
How do you find the number of integral solutions of the equation 2x + 3y = 763?
2x + 3y = 763
=> y = (763 - 2x)/3
It has infinite integral solutions as there are infinite integral values of 'x' for which 'y' is an integer.
But the equation has finite number of positive integral solutions and I have solved for it.
Now, for 'y' to be an integer, (763-2x) must be a multiple of 3.
A little observation tells us that it happens when
763-2x=759,753,747,741,735,729..15,9 and 3.
=> x=2,5,8,11,14,17...371,374,377,380
For each value of 'x', y can be calculated.
The values of 'x' forms an A.P.
so,
380 = 2 + (n-1)3
=>n=127.
Hence, there are 127 solutions to the equation.
=> y = (763 - 2x)/3
It has infinite integral solutions as there are infinite integral values of 'x' for which 'y' is an integer.
But the equation has finite number of positive integral solutions and I have solved for it.
Now, for 'y' to be an integer, (763-2x) must be a multiple of 3.
A little observation tells us that it happens when
763-2x=759,753,747,741,735,729..15,9 and 3.
=> x=2,5,8,11,14,17...371,374,377,380
For each value of 'x', y can be calculated.
The values of 'x' forms an A.P.
so,
380 = 2 + (n-1)3
=>n=127.
Hence, there are 127 solutions to the equation.