We are given the following system of equations:
[tex]\begin{gathered} g(x)=3x+2 \\ f(x)=|x-1|+1 \end{gathered}[/tex]
A solution of the system is the value of "x" for which:
[tex]g(x)=f(x)[/tex]
This means the point where the functions yield the same number. To determine if the point:
[tex](x,y)=(1,5)[/tex]
This means that we need to substitute the value x = 1 and both functions must be equal to 5. Substituting in g(x) we get:
[tex]g(1)=3(1)+2=3+2=5[/tex]
Now we substitute in the function f(x):
[tex]f(1)=|1-1|+1=0+1=1[/tex]
Since:
[tex]g(1)\ne f(1)\ne5[/tex]
This point is not a solution of the system.
