Question 253004
x^2 - y^2 = 28 (first equation)
x - y = 8 (second equation)


solve for x in second equation to get:


x = y+8


substitute for x in first equation to get:


x^2 - y^2 = 28 becomes:


(y+8)^2 - y^2 = 28


simplify by performing indicated operations to get:


y^2 + 16y + 64 - y^2 = 28


combine like terms to get:


16y + 64 = 28


subtract 64 from both sides to get:


16y = 28-64 = -36


divide both sides by 16 to get:


y = -36/16


substitute in second equation to get:


x - y = 8 becomes:


x - (-36/16) = 8.


simplify by performing indicated operations to get:


x + 36/16 = 8


subtract 36/16 from both sides to get:


x = 8 - 36/16 = 128/16 - 36/16 = 92/16.


you have:


x = 92/16
y = -36/16


substitute in first equation to get:


x^2 - y^2 = 28 becomes:


(92/16)^2 - (-36/16)^2 = 28


this becomes:


33.0625 - 5.0625 = 28 confirming that the values for x and y are good.


the question was:


what is the average of x and y?


the average of x and y = {{{((92/16) + (-36/16))/2 = ((92/16) - (36/16))/2 = (56/16)/2 = (56/32) = 1.75}}}