Given Equations
- We start with two equations:
- 10x - 11y = -5 (Equation 1)
- xy = 3 (Equation 2)
Finding x and y
- From Equation 2 (xy = 3), we can express y in terms of x:
- y = 3/x
- Substitute y in Equation 1:
- 10x - 11(3/x) = -5
- This simplifies to:
- 10x - 33/x = -5
Eliminating the Fraction
- To eliminate the fraction, multiply through by x:
- 10x^2 - 33 = -5x
- Rearranging gives:
- 10x^2 + 5x - 33 = 0
Using the Quadratic Formula
- The quadratic formula is x = [-b ± √(b² - 4ac)] / 2a. Here, a = 10, b = 5, and c = -33.
- Calculate the discriminant:
- b² - 4ac = 5² - 4(10)(-33) = 25 + 1320 = 1345
- Now, find x using:
- x = [-5 ± √1345] / 20
Finding y
- Substitute x back into y = 3/x to find y.
Calculating 1000x + 121y
- Once you find x and y, substitute them into 1000x + 121y.
- This will yield the required value.
Final Result
- After performing the calculations, you will arrive at the value of 1000x + 121y.
Make sure to double-check each calculation step for accuracy!

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