Question

solve 1/2x + 1/4y- 1/3z=1/4 ;1/x=1/3y; 1/x-1/5y+4/z=2*2/5​

Answer 1

Answer:

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Answer 2

Answer:

x = 77/17

y = 77/51

z = 77/445

Step-by-step explanation:

Given equations are:

$\frac{1}{2x}$ +  $\frac{1}{4y}$ -  $\frac{1}{3z}$ =  $\frac{1}{4}$        

$\frac{1}{x}$ =  $\frac{1}{3y}$                        

 $\frac{1}{x}$ -  $\frac{1}{5y}$ +  $\frac{4}{z}$ =  $\frac{12}{5}$​          

Let  $\frac{1}{x}$ be a, $\frac{1}{y}$ be b and $\frac{1}{z}$ be c

Therefore, the equations become

a/2 +b/4 - c/3 = 1/4 => 6a + 3b - 4c = 3 -----(i)

a = b/3  => 3a = b                                     ---(ii)

a - b/5 + 4c = 12/5 => 5a - b + 20c = 12   --(iii)

Putting b as 3a in equation (i) and (iii)

=> 6a + 3(3a) - 4c = 3  => 15a - 4c = 3      --(iv)

=> 5a - 3a + 20c = 12  => 2a + 20c = 12   --(v)

Multiplying equation (iv) by 5

=> 75a - 20c = 15

=> 2a + 20c = 12

Adding the above equations, we get

77a = 17

=> a = 17/77

=> b = 3*a = 3*(17/77) = 51/77

=> 20c = 12 - 2(17/77) =  890/77 => c = 445/77

As x, y, z is the reciprocal of  a, b, c respectively,

Therefore x = 77/17

y = 77/51

z = 77/445