Answer:
The total number of solutions is one
Step-by-step explanation:
we have
[tex]f(x)=-\frac{11}{3}x+ \frac{11}{3}[/tex]
[tex]g(x)=x^{3}+2x^{2}-x-2[/tex]
To solve the system of equations equate f(x) and g(x)
[tex]f(x)=g(x)[/tex]
The solution of the system of equations is the intersection points both graphs
Using a graphing tool
see the attached figure
The solution of x
[tex]x=1[/tex]
There is only one point of intersection both graphs
therefore
The total number of solutions is one
