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).
