The shaded area is 34.66 sq. units.
<h2>
Linear system</h2>
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.
<h3>
To find </h3>
The shaded area is shown in the graph.
<h3>How to find a shaded area?</h3>
A line y = mx + c
For dashed line, the slope (m) is given by
![\rm m = \dfrac{y_{2} -y_{1} }{x_{2} -x_{1} } \\\\m = \dfrac{3-0}{1-0} \\\\m = 3](https://tex.z-dn.net/?f=%5Crm%20m%20%3D%20%5Cdfrac%7By_%7B2%7D%20-y_%7B1%7D%20%7D%7Bx_%7B2%7D%20-x_%7B1%7D%20%7D%20%5C%5C%5C%5Cm%20%3D%20%5Cdfrac%7B3-0%7D%7B1-0%7D%20%5C%5C%5C%5Cm%20%3D%203)
And c = 0 because the line is passing through the origin.
so the equation is 3y = x
For x = -1 then y = -1/3
Then
The base and height of the triangle will be 16/3 and 4.
And the height of the trapezium and the sum of the parallel side are 4 and 12.
Then the shaded area will be
![\rm Shaded\ area\ =\ area\ of\ trapezium\ +\ area\ of\ triangle\\\\Shaded\ area\ = \dfrac{1}{2} (sum\ of\ parallel\ sidess)* height +\dfrac{1}{2} base *height\\\\Shaded\ area\ = \dfrac{1}{2} *12*4 +\dfrac{1}{2} * \dfrac{16}{3} *4\\\\Shaded\ area\ = 34.66](https://tex.z-dn.net/?f=%5Crm%20Shaded%5C%20area%5C%20%3D%5C%20area%5C%20of%5C%20trapezium%5C%20%2B%5C%20area%5C%20of%5C%20triangle%5C%5C%5C%5CShaded%5C%20area%5C%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%20%28sum%5C%20of%5C%20parallel%5C%20sidess%29%2A%20height%20%2B%5Cdfrac%7B1%7D%7B2%7D%20base%20%2Aheight%5C%5C%5C%5CShaded%5C%20area%5C%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%20%2A12%2A4%20%2B%5Cdfrac%7B1%7D%7B2%7D%20%2A%20%5Cdfrac%7B16%7D%7B3%7D%20%2A4%5C%5C%5C%5CShaded%5C%20area%5C%20%3D%2034.66)
Thus, the shaded area is 34.66 sq. units.
More about the linear system link is given below.
brainly.com/question/20379472