Question

Solve the following simultaneous equations.

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

ii. (x/3) + 5y = 13; 2x + (y/2) = 19

iii. (2/x) + (3/y) = 13; (5/x) - (4/y) = -2

Answer 1

i. (x/3) + (y/4) = 4

Multiplying both sides by 12, 4x + 3y = 48 …(i)

(x/2) - (y/4) = 1

Multiplying both sides by 8, 

4x – 2y = 8 …..(ii) 

Subtracting equation (ii) from (i),

∴ y = 8 

Substituting y = 8 in equation (ii),

4x – 2y = 8 

∴ 4x – 2(8) = 8 

∴ 4x – 16 = 8 

∴ 4x = 8 + 16 

∴ 4x = 24

∴ x = 24/4

∴ x = 6 

∴ (6, 8) is the solution of the given equations.

ii. (x/3) + 5y = 13 

Multiplying both sides by 3, 

x + 15y = 39 …(i) 

2x + (y/2) = 19 

Multiplying both sides by 2, 

4x + y = 38 …….(ii) 

Multiplying equation (i) by 4, 

4x + 60y = 156 …(iii) 

Subtracting equation (ii) from (iii), 

4x + 60y = 156 

4x + y = 38

∴ y = 2 

Substituting y = 2 in equation (i), 

x + 15y = 39 

∴ x + 15(2) = 39 

∴ x + 30 = 39 

∴ x = 39 – 30 = 9 

∴ (9,2) is the solution of the given equations. 

iii. (2/x) + (3/y) = 13

Multiplying both sides by 5,

So, 10/x = 8 x 3 - 4