Question

Can anyone plzzzz help me with this question of linear equation in two varaiable plzzzzzz... Its very important... Plz solve it for me.... ​

Answer 1

That's not a linear system, but you have an awesome school system for giving you this problem.

`\frac 5 y - \frac 2 x = \frac{13}6`

Multiply by 6xy to clear the fractions.

`30x - 12y = 13 xy`

That's a second degree equation, also known as a conic. That one happens to be a hyperbola.

`30x = y(13 x +12)`

`y = (30x)/(13 x + 12)`

Let's clear the fractions from the second equation, multiplying out common denominator xy:

`\frac {36} x - \frac {24} y = 1`

`36y - 24 x = xy`

We are being asked to find the meet of two hyperbolas, so we expect two answers, a quadratic equation.

Substituting,

`36 \left( (30x)/(13 x + 12) \right) - 24 x = x \left( (30x)/(13 x + 12) \right)`

`36(30x) -24 x(13x + 12) = 30x^2`

`1080 x - 312 x^2- 288 x = 30x^2`

`x(792 - 342 x)= 0`

`x = 0 \textrm{ or } x=792/342 = (44)/(19)`

We have to rule out x=0 because it's in the denominator.

`y = (30x)/(13 x + 12) = (30(44/19))/(13(44/19)+12)`

`y = (33)/(20)`

Answer: (44/19, 33/20)