If x and y are natural numbers, then find the number of ordered pairs (x, y) which satisfy the equation 3x − 7y = 20 and the inequality x + y ≤ 30.
same .....3x=30-7y.....x=3,y=3...x=10,y=0 not a soln... so only 1 soln
Well if you will eliminate y then you will get 10x = 20 + 7*c where c is value less than 30 or 30,,
Now x will be integral value only if RHS will be multiple of 10, so we can put c = 30 or 20 or 10.. but not 0 or less as we want natural number. Therefore, ans is 3
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