Question

determine the solution to the system of equations graphed below and explain your reasoning g(x)=3x+2 f(x)=|x-1|+1​

Answer 1

Answer:

(0, 1)

Step-by-step explanation:

To find the solution to these 2 functions, we just set up an equation where they're equal to each other:

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

Then, isolate the absolute value:

3x+1 = |x-1|

Now, to get rid of the absolute value sign, we can set the right-hand side to be the positive or negative version of itself.

First, let's set it to the negative version of itself:

3x+1 = -x+1

4x = 0

x = 0

Then, let's set it to the positive version of itself:

3x+1 = x-1

2x = -2

x = -2

We can now plug the x as 0 and -2 into any of the 2 equations above to find the solution for y:

3(0)+1 = 1, so the first solution will be (0, 1)

3(-2)+2 = -4.

You might be tempted to say that -4 is the y value for the 2nd solution, but notice that |x-1| will never be less than 0, so that would not work. Therefore, x = -2 isn't a solution either, which means it's an extraneous solution.

In conclusion, the solution to these equations is (0, 2).

Answer 2

By finding the point where the graphs intercept, we will see that the solution of the system of equations is the point (0, 2).

How to find the solutions of a system of equations graphically?

The solutions of a system of equations are the points where the graphs of the different equations intercept when graphed.

Below you can see the graph of the system:

• g(x) = 3x + 2   (green)
• f(x) = |x - 1| + 1    (blue).

There you can see that we have only one intersection point at x = 0, y = 2, then we can conclude that our system has only one solution, and the solution is the point (0, 2).

If you want to learn more about systems of equations, you can read:

https://brainly.com/question/13729904