That's not a linear system, but you have an awesome school system for giving you this problem.
![\dfrac 5 y - \dfrac 2 x = \dfrac{13}6](https://tex.z-dn.net/?f=%20%5Cdfrac%205%20y%20-%20%5Cdfrac%202%20x%20%3D%20%5Cdfrac%7B13%7D6%20)
Multiply by 6xy to clear the fractions.
![30x - 12y = 13 xy](https://tex.z-dn.net/?f=%2030x%20-%2012y%20%3D%2013%20xy%20)
That's a second degree equation, also known as a conic. That one happens to be a hyperbola.
![30x = y(13 x +12)](https://tex.z-dn.net/?f=%2030x%20%3D%20y%2813%20x%20%2B12%29)
![y = \dfrac{30x}{13 x + 12}](https://tex.z-dn.net/?f=%20y%20%3D%20%5Cdfrac%7B30x%7D%7B13%20x%20%2B%2012%7D)
Let's clear the fractions from the second equation, multiplying out common denominator xy:
![\dfrac {36} x - \dfrac {24} y = 1](https://tex.z-dn.net/?f=%20%5Cdfrac%20%7B36%7D%20x%20-%20%5Cdfrac%20%7B24%7D%20y%20%3D%201%20)
![36y - 24 x = xy](https://tex.z-dn.net/?f=%2036y%20-%2024%20x%20%3D%20xy)
We are being asked to find the meet of two hyperbolas, so we expect two answers, a quadratic equation.
Substituting,
![36 \left( \dfrac{30x}{13 x + 12} \right) - 24 x = x \left( \dfrac{30x}{13 x + 12} \right)](https://tex.z-dn.net/?f=36%20%5Cleft%28%20%5Cdfrac%7B30x%7D%7B13%20x%20%2B%2012%7D%20%5Cright%29%20-%2024%20x%20%3D%20x%20%5Cleft%28%20%5Cdfrac%7B30x%7D%7B13%20x%20%2B%2012%7D%20%5Cright%29)
![36(30x) -24 x(13x + 12) = 30x^2](https://tex.z-dn.net/?f=36%2830x%29%20-24%20x%2813x%20%2B%2012%29%20%3D%2030x%5E2)
![1080 x - 312 x^2- 288 x = 30x^2](https://tex.z-dn.net/?f=1080%20x%20-%20312%20x%5E2-%20288%20x%20%3D%2030x%5E2)
![x(792 - 342 x)= 0](https://tex.z-dn.net/?f=x%28792%20-%20342%20x%29%3D%200)
![x = 0 \textrm{ or } x=792/342 = \dfrac{44}{19}](https://tex.z-dn.net/?f=%20x%20%3D%200%20%5Ctextrm%7B%20or%20%7D%20x%3D792%2F342%20%3D%20%5Cdfrac%7B44%7D%7B19%7D)
We have to rule out x=0 because it's in the denominator.
![y = \dfrac{30x}{13 x + 12} = \dfrac{30(44/19)}{13(44/19)+12}](https://tex.z-dn.net/?f=y%20%3D%20%5Cdfrac%7B30x%7D%7B13%20x%20%2B%2012%7D%20%3D%20%5Cdfrac%7B30%2844%2F19%29%7D%7B13%2844%2F19%29%2B12%7D)
![y = \dfrac{33}{20}](https://tex.z-dn.net/?f=y%20%3D%20%5Cdfrac%7B33%7D%7B20%7D)
Answer: (44/19, 33/20)
Explanation: Division property of equality is dividing both sides of an equation by the same non-zero number does not change the equation.
a÷c=b÷c for c≠0
<u><em>First, you divide by 3 both sides of an equation.</em></u>
<u><em>3y/3=24/3</em></u>
<u><em>Then, simplify.</em></u>
<u><em>24/3=8</em></u>
<u><em>8*3=24</em></u>
<u><em>24/8=3</em></u>
<u><em>y=8 is the final answer.</em></u>
<u><em>Hope this helps!</em></u>
<u><em>Thanks!</em></u>
<u><em>Have a great day!</em></u>
Multiply 370 by 0.16 get get 16%
370 x 0.16 = 59.2%
If we're only counting 5 vowels (A, E, I, O, U) and 20 consonants (everything else, minus T), then there are
![\dbinom52=\dfrac{5!}{2!(5-2)!}=10](https://tex.z-dn.net/?f=%5Cdbinom52%3D%5Cdfrac%7B5%21%7D%7B2%21%285-2%29%21%7D%3D10)
ways of picking the vowels, and
![\dbinom{20}2=\dfrac{20!}{2!(20-2)!}=190](https://tex.z-dn.net/?f=%5Cdbinom%7B20%7D2%3D%5Cdfrac%7B20%21%7D%7B2%21%2820-2%29%21%7D%3D190)
ways of picking the consonants.
We want the word to start with T, and we'll allow any arrangement of the other 4 letters, so that the total number of words is
![4!\dbinom52\dbinom{20}2=\boxed{45,600}](https://tex.z-dn.net/?f=4%21%5Cdbinom52%5Cdbinom%7B20%7D2%3D%5Cboxed%7B45%2C600%7D)
Keep in mind that this means words like TRIES and TIRES are treated as different.