Solution to the systems of equations,
g(x)=3x+2
f(x)=|x-1|+1

Hi there! :)

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.

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