On solving the linear system, for the value of y = 15, the value of x is 200. The correct option is D.
<h3>What is the linear system?</h3>
It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.
Given
The linear equation is shown below.
![\rm \dfrac{1}{5}x - \dfrac{2}{3}y = 30](https://tex.z-dn.net/?f=%5Crm%20%5Cdfrac%7B1%7D%7B5%7Dx%20-%20%5Cdfrac%7B2%7D%7B3%7Dy%20%3D%2030)
The equation can be written as
![\rm 3x - 10y = 450\\](https://tex.z-dn.net/?f=%5Crm%203x%20-%2010y%20%3D%20450%5C%5C)
For y = 15, the value of x will be.
![\begin{aligned} \rm 3x - 10*15 &= 450\\\\\rm 3x - 150 &= 450 \\\\\rm 3x &= 600\\\\\rm x &= 200\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20%5Crm%203x%20-%2010%2A15%20%26%3D%20450%5C%5C%5C%5C%5Crm%203x%20-%20150%20%26%3D%20450%20%5C%5C%5C%5C%5Crm%203x%20%26%3D%20600%5C%5C%5C%5C%5Crm%20x%20%26%3D%20200%5C%5C%5Cend%7Baligned%7D)
The value of x is 200.
Thus, option D is correct.
More about the linear system link is given below.
brainly.com/question/20379472