Question

Determine whether the point (2, 2) is a solution to the system of equations. Explain your reasoning in complete sentences. Prove you answer mathematically by verifying the point (2,2) with the given equations by inspection (show all work). If (2,2) is not the solution to the system, what is the solution and how do you know?

Answer 1

(0,2) is the solution of the given functions.

Explanation:

We have been given two functions f(x)=|x-1|+1 and g(x)=3x+2

To find the solution of the two functions mathematically, we will equate the given functions:

3x+2=|x-1|+1

3x+1=|x-1|

When we will open the modulus function we will have two values +, -

In positive case:

3x+1 =x-1

2x=-2

x=-1

Now, substitute x=-1 in g(x)=3x+2 we get

g(-1)=3(-1)+2=-1

Hence, (-1,-1) is the solution of the given functions.

In negative case:

Now, 3x+1=-(x-1)

3x+1=-x+1

4x=0

x=0

Now, put x=0 in g(x)=3x+2 we get

g(0)=3(0)+2=2

We have another solution: (0,2)

The point (2,2) is not the solution.

And graphically, the solution of two functions is their intersection point which is (0,2)

Hence, (0,2) is the solution of the function.