Hi there! :)
[tex]\large\boxed{\text{ x = 0, or (0, 2)}}[/tex]
The solution of g(x) = 3x + 2 and f(x) = |x - 1| + 1 is where the two lines intersect.
According to the graph, the functions intersect at the point (0, 2), or x = 0. This is the solution to the system of equations.
We could also prove this algebraically by setting the two equations equal to each other:
3x + 2 = | x - 1 | + 1
Assume the absolute value function is negative:
3x + 2 = -(x - 1) + 1
Simplify:
3x + 2 = -x + 2
Add x to both sides:
4x + 2 = 2
Subtract 2 from both sides:
4x = 0
x = 0. This is the solution to the system.
