Answer:
<h3>Graph A is correct.</h3>
Step-by-step explanation:
We are given the system of inequality,
![x+y=4\\\\2x+3y=18](https://tex.z-dn.net/?f=x%2By%3D4%5C%5C%5C%5C2x%2B3y%3D18)
Now, it is required to find the graph of the system of equations.
We have the equations,
............(1)
.............(2)
Multiplying (1) by 2 and subtracting the equations gives us,
![2x+2y-2x-3y=8-18\\-y=-10\\y=10](https://tex.z-dn.net/?f=2x%2B2y-2x-3y%3D8-18%5C%5C-y%3D-10%5C%5Cy%3D10)
Substituting the value of y in any equation, we get,
![x + 10 = 4\\x=4-10\\x=-6](https://tex.z-dn.net/?f=x%20%2B%2010%20%3D%204%5C%5Cx%3D4-10%5C%5Cx%3D-6)
Thus, the solution of the system of equations is (-6,10).
As we have that the point (-6,10) will lie in the second quadrant.
So, the graphs of the equations must intersect in the second quadrant.
Moreover, the slope intercept forms of the equations are given by,
![y=-x+4](https://tex.z-dn.net/?f=y%3D-x%2B4)
![y =\frac{-2}{3}x+6](https://tex.z-dn.net/?f=y%20%3D%5Cfrac%7B-2%7D%7B3%7Dx%2B6)
Thus, the slope of the equations are -1 and
.
Then, the graphs of the equations must be decreasing.
Hence, the correct option is 'Graph A' given below.