Answer: [tex]y=5[/tex]
Step-by-step explanation:
You need to analize the figure carefully in order to understand the information given in the exercise.
According to the data given, you know that the lenght of the side BD of the triangle ABD is:
[tex]BD=16[/tex]
You can notice in the figure the lenght BD is the sum of the lenght BC and the lenght CD.
Knowing that, you can can write the following equation:
[tex]BD=BC+CD[/tex]
Since:
[tex]BC=2y-2\\\\CD=y+3[/tex]
You can make the substitution into [tex]BD=BC+CD[/tex] and then solve for "y" in order to find its value.
The result is:
[tex]16=(2y-2)+(y+3)\\\\16=3y+1\\\\16-1=3y\\\\\frac{15}{3}=y\\\\y=5[/tex]
