Answer:
y = 2
Step-by-step explanation:
[tex]\text{If}\ \overrightarrow{BD}\ \text{is the angle bisector of}\ \angle ABC,\ \text{then we have two equations:}\\\\(1)\qquad2x+y=14+y\\(2)\qquad5x-y=x+13y\\------------------\\\\(1)\\2x+y=14+y\qquad\text{subtract}\ y\ \text{from both sides}\\2x=14\qquad\text{divide both sides by 2}\\\boxed{x=7}\\\\\text{Put the value of x to (2):}\\\\5(7)-y=7+13y\\35-y=7+13y\qquad\text{subtract 35 from both sides}\\-y=-28+13y\qquad\text{subtract 13y from both sides}\\-14y=-28\qquad\text{divide both sides by (-14)}\\\boxed{y=2}[/tex]
