Solve the following pairs of linear equations: 99x + 101y = 499xy 101x + 99y = 501xy

Given, 99x + 101y = 499xy 101x + 99y = 501xy First we note that x = 0, y = 0 is a solution of equations. Now when x ≠ 0 and y ≠ 0. Dividing the above equations by xy we get, .......(i) .......(ii) Substituting in both equations and multiplying eq. (i) by 101 and (ii) by 99 we get, 9999q + 10201p = 50399 ......(iii) 9999q + 9801p = 49599 ......(iv) Subtracting (iv) from (iii) we get, ⇒ 9999q + 10201p - (9999q + 9801p) = 50399 - 49599 ⇒ 9999q - 9999q + 10201p - 9801p = 800 ⇒ 400p = 800 ⇒ p = 2. Substituting value of p in (iii) we get, ⇒ 9999q + 10201(2) = 50399 ⇒ 9999q + 20402 = 50399 ⇒ 9999q = 29997 ⇒ q = 3. . Hence, x = 0, y = 0 and x =

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Solve the following pairs of linear equations:
3x + 14y = 5xy
21y - x = 2xy

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Solve the following pairs of linear equations:
3x + 5y = 4xy
2y - x = xy.

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Mathematics

Solve the following pairs of linear equations:
99x + 101y = 499xy
101x + 99y = 501xy

Linear Equations

Related Questions

Solve the following pairs of linear equations:
3x + 14y = 5xy
21y - x = 2xy

Solve the following pairs of linear equations:
3x + 5y = 4xy
2y - x = xy.

Mathematics

Solve the following pairs of linear equations:99x + 101y = 499xy101x + 99y = 501xy

Linear Equations

Related Questions

Solve the following pairs of linear equations:3x + 14y = 5xy21y - x = 2xy

Solve the following pairs of linear equations:3x + 5y = 4xy2y - x = xy.

Solve the following pairs of linear equations:
99x + 101y = 499xy
101x + 99y = 501xy

Solve the following pairs of linear equations:
3x + 14y = 5xy
21y - x = 2xy

Solve the following pairs of linear equations:
3x + 5y = 4xy
2y - x = xy.