Question

Hi how to solve this simultaneous equation

Answer 1

`\large \boxed{\sf \ \ x=\pm8 \ \ or \ \ x=\pm2 \ \ }`

Explanation:

Hello, please consider the following.

First of all, we can assume that x and y are different from 0, as we cannot divide by 0.

And from the first equation we can write y as a function of x as below.

`y=(16)/(x)`

And then, we replace it in the second equation to get.

`(x)/((16)/(x))+((16)/(x))/(x)=(17)/(4)\\\\<=> (x^2)/(16)+(16)/(x^2)=(17)/(4)\\\\\text{*** We multiply by }16x^2 \text{ both sides ***}\\\\x^4+16*16=(17*16)/(4)x^2\\\\x^4-68x^2+3600=0\\\\\text{*** The product of the zeroes is 3600 = 64*4 and the sum is 64+4=68 ***}\\\\\text{*** So we can factorise *** }\\\\x^4-64x^2-4x^2+3600=x^2(x^2-64)-4(x^2-64)=(x^2-64)(x^2-4)=0\\\\x^2=64=8^2 \ \ or \ \ x^2=4\\\\x=\pm8 \ \ or \ \ x=\pm2\\`

Hope this helps.

Do not hesitate if you need further explanation.

Thank you