Given right triangle a w/a hypotenuse length of 3y + x and a leg of y-x, and right triangle b, w/ a hypotense length of y+5 and a leg length of x+5, for what values of x and y are the triangles congruent by hl?

We use the law of correspondence that is 
Hypotenuse = Hypotenuse Leg = Leg 

3y + x = y + 5 
and 
y - x = x + 5  work on your first problem to find x 
x = -2y + 5 
now you can plug this in to your second equation to sub in for the x 
y - ( -2y + 5 ) = ( -2y + 5 ) + 5 y + 2y - 5 = -2y + 10 3y - 5 = -2y + 10 5y = 15 y = 3 
Now you can plug back in to solve for x 

3y + x = y + 5 3(3) + x = (3) + 5 9 + x = 8 x = -1 
so y = 3 and x = -1