Step 1
The point of intersection of the lines of both functions shows the solution to both functions.
Therefore, from the graph the solution in the form of (x,y) is
Step 2
From the question, we are required to find out if the point (1,1) is a solution to the system of equations.
We can decide on the answer in 2 ways
![\begin{gathered} 1)\text{ (1,1) is not a solution of the system of equations since it is not a point of intersection of both lines in the graph} \\ 2)\text{ We substitute the value of x, 1 into both equations and solve to s}ee\text{ if we will get y=1 in both equations} \end{gathered}]()
![\begin{gathered} g(x)\text{ = 3x+2} \\ g(1)=3(1)+2 \\ g(1)=\text{ 3+}2 \\ g(1)\text{ = }5 \\ f(x)\text{ = }\mleft|x-1\mright|+1_{} \\ f(1)\text{ = }\mleft|1-1\mright|+1 \\ f(1)\text{ = 0+1} \\ f(1)\text{ = 1} \\ \text{Since both equations did not give us the same values of y then the points (1,1) is not a solution to the system of equations} \end{gathered}]()
Therefore, the points (1,1) is not a solution to the system of equations.