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

Given, 3x + 14y = 5xy .......(i) 21y - x = 2xy ........(ii) First we note that x = 0, y = 0 is a solution of the equations. Now when x ≠ 0 and y ≠ 0. Dividing eq. (i) by xy we get, Dividing eq. (ii) by xy we get, Substituting in eq. (iii) and (iv) we get, 3b + 14a = 5 ........(v) 21a - b = 2 .........(vi) Multiplying eq. (vi) by 3 we get, 63a - 3b = 6 .......(vii) Adding eq. (v) and (vii) we get, ⇒ 3b + 14a + (63a - 3b) = 5 + 6 ⇒ 77a = 11 ⇒ a = . Substituting value of a in eq. (v) we get, ⇒ 3b + = 5 ⇒ 3b + 2 = 5 ⇒ 3b = 3 ⇒ b = 1. Hence, x = 0, y = 0 and x = 7, y = 1.

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

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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:
3x + 14y = 5xy
21y - x = 2xy

Linear Equations

Related Questions

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

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

Mathematics

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

Linear Equations

Related Questions

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

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

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

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

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