SOLUTION: The figure shows an equilateral triangle with its sides as indicated. Find the length of each side of the triangle 2x-7 X+y-9 Y+5

Since the triangle is equilateral, the three sides have equal lengths.


It gives you this system of two equations in two unknowns:


2x - 7 = x + y - 9    (1)
2x - 7 = y + 5        (2)


Simplify by collecting the unknown variables on the left side and the constant terms on the right


 x - y = -2           (1')
2x - y = 12           (2')


To solve the system, apply the Elimination method.
For it, subtract equation (1') from equation (2').  Then the " y " terms will cancel each other, and you will obtain 

2x - x = 12 - (-2),     or

x = 14.


Now you can calculate the side length as  (2x-7) = 2*14 - 7 = 21.


Answer.  Each side of the given equilateral triangle is 21 units long.