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If 101x + 99y = 703 and 99x + 101y = 697; then the values of x and y respectively are 
  • a)
    5, –2 
  • b)
    2, -5 
  • c)
    2, 5 
  • d)
    None of the above 
Correct answer is option 'D'. Can you explain this answer?
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If 101x + 99y = 703 and 99x + 101y = 697; then the values of x and y r...
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If 101x + 99y = 703 and 99x + 101y = 697; then the values of x and y r...
Problem Statement
We have two equations:
1. 101x + 99y = 703
2. 99x + 101y = 697
We need to find the values of x and y.
Step 1: Solve the Equations
To solve these equations, we can use the method of elimination or substitution. Here, we will use elimination.
Multiplying the first equation by 99 and the second by 101:
- (99)(101x + 99y) = (99)(703)
- (101)(99x + 101y) = (101)(697)
This gives us:
- 9999x + 9801y = 69597
- 9999x + 10201y = 70397
Now, we can subtract the first equation from the second:
9801y - 10201y = 70397 - 69597
This simplifies to:
- 401y = 800
So, we find that:
y = -2
Step 2: Substitute the Value of y
Now, substitute y back into one of the original equations to find x. Using the first equation:
101x + 99(-2) = 703
This simplifies to:
101x - 198 = 703
Adding 198 to both sides gives:
101x = 901
So, we find that:
x = 9
Final Values
The calculated values are:
- x = 9
- y = -2
Since neither (5, -2), (2, -5), nor (2, 5) matches our results, the correct answer is indeed option 'D': None of the above.
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If 101x + 99y = 703 and 99x + 101y = 697; then the values of x and y respectively area)5, –2b)2, -5c)2, 5d)None of the aboveCorrect answer is option 'D'. Can you explain this answer?
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