[latexpage]

# Algebra

The equation 11x + 67y = 133 has

1. two integral solutions for 0 < x < 50
2. no integral solutions for 10 < y < 20
3. an integral solution for 100 < x < 200
4. no integral solutions for y < 0

### Solve our previous ‘questions of the day’

1. Abhishek Tandon

Option b?

1. What approach did you use ? Abhishek

1. Abhishek Tandon

Raman Sir,
While solving again I got it where I went wrong. Please correct me if I am wrong.
I tried this way
11x+67y=133

(x,y):……..(-61,12), (6,1), (6+67,1-11),….
(x,y): (6,1), (73,-10), (130,-21), (197,-32)…..

From above values I eliminated options
Option 1: eliminated because there is only one integral solution in that x range

Option2: eliminated because for y=12 x=-61 hence it is in range so there is an integral solution

Option 3: satisfying because there are 2 integral solutions in that range

Option 4: eliminated because there are many integral solutions for y<0

1. Perfect Abhishek 🙂

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