Question

Solve the following simultaneous equations:

i.  7x-2y/xy = 5; 8x + 7y/xy = 15

ii. 1/2(3x+4y) + 1/5(2x-3y) = 1/4; 5/(3x + 4y) - 2/(2x-3y) = -3/2

Answer 1

i. The given simultaneous equations are

∴ Equations (i) and (ii) become 7q – 2p = 5 …(iii) 8q + 7p = 15 …(iv) 

Multiplying equation (iii) by 7, we get 

49q – 14p = 35 …(v) 

Multiplying equation (iv) by 2, we get 

16q + 14p = 30 …(vi) 

Adding equations (v) and (vi), we get

   49q – 14p = 35

+ 16q + 14p = 30/65q =65

∴ q = 65/65 = 1

Substituting q = 1 in equation (iv), we get 8(1) + 7p = 15 

∴ 8 + 7p = 15 

∴ 7p = 15 – 8 

∴ 7p = 7

∴ p = 7/7 = 1 

∴ (P, q) = (1,1)

Resubstituting the values of p and q, we get 1 = 1/x and 1 =1/y 

∴ x = 1 and y = 1 

∴ (x, y) = (1, 1) is the solution of the given simultaneous equations.

ii The given simultaneous equations are

∴ 4q = 4

∴ q = 4/4 = 1

∴ (p, q) = (1/10, 1)

Resubstituting the values of p and q, we get

1/10= 1/3x + 4y and 1 = 1/2x - 3y 

∴ 3x + 4y = 10 …(v) 

and 2x – 3y = 1 …(vi) 

Multiplying equation (v) by 3, we get 

9x + 12y = 30 …(vii) 

Multiplying equation (vi) by 4, we get 

8x – 12y = 4 …(viii) 

Adding equations (vii) and (viii), we get 

9x + 12y = 30

∴ (x, y) = (2, 1) is the solution of the given simultaneous equations.