Question

4 / X + 3y = 14 and 3/x +4y=23​

Answer 1

Answer:

$\bold\red{a=\frac{-7}{13}}\:and\:\bold\red{y=\frac{50}{7}}$

Step-by-step explanation:

The given pair of linear equations are,

$\frac{4}{x}+3y=14\:\:\:.............(i)\\\\\frac{3}{x}+4y=23\:\:\:...............(ii)$

Let, us take (1/x) equals to 'a'

Therefore, the equations, we have are,

4a + 3y = 14 ..........(iii)

3a + 4y = 23 ............(iv)

Multiplying eqn (iii) with 3 and eqn (iv) with 4,

we get,

12a + 9y = 42 ............(v)

12a + 16y = 92 ............(vi)

Now, subtract eqn (v) from (vi) ,

we get,

16y - 9y = 92 - 42

=> 7y = 50

=> y = 50/7

Therefore,

=> 4a + 150/7 = 14

=> 4a = 14- 150/7

$= > 4a = \frac{98 - 150}{7} \\ \\ = > a = \frac{ - 52}{28} \\ \\ = > a = \frac{ - 13}{7}$

But, a = 1/x

$=> \frac{1}{x}=\frac{-13}{7}\\\\=> a=\frac{-7}{13}$

Hence,

$\bold{a=\frac{-7}{13}}\:and\:\bold{y=\frac{50}{7}}$