Answer:
Graph A is correct.
Step-by-step explanation:
We are given the system of inequality,
[tex]x+y=4\\\\2x+3y=18[/tex]
Now, it is required to find the graph of the system of equations.
We have the equations,
[tex]x + y = 4[/tex] ............(1)
[tex]2x + 3y = 18[/tex] .............(2)
Multiplying (1) by 2 and subtracting the equations gives us,
[tex]2x+2y-2x-3y=8-18\\-y=-10\\y=10[/tex]
Substituting the value of y in any equation, we get,
[tex]x + 10 = 4\\x=4-10\\x=-6[/tex]
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,
[tex]y=-x+4[/tex]
[tex]y =\frac{-2}{3}x+6[/tex]
Thus, the slope of the equations are -1 and [tex]\frac{-2}{3}[/tex].
Then, the graphs of the equations must be decreasing.
Hence, the correct option is 'Graph A' given below.
