1. X

^{2}+ y^{2}= 8 (equation 1) 2. X - y = 0 (equation 2) x = 0 + y (express x in terms of y from equation 2) x = y (collect terms) x^{2}+ x^{2}= 8 (substitute value of y into equation 1) x^{4}= 8 (apply exponent law) (x^{4})^{(1/4) }= 8^{(1/4)}(eliminate the exponent) x = 2 (simplify) We know that x = y. This concludes that y = 2.__Check:__x^{2}+ y^{2}= 8 (eqaution 1) 2^{2}+ 2^{2}= 8 (substitue values) 4 + 4 = 8 (simplify exponents) 8 = 8 (collect terms; correct!) x - y = 0 (equation 2) 2 - 2 = 0 (substitue values) 0 = 0 (collect terms; correct!) Or perhaps you intended: 1. 2x + 2y = 8 (equation 1) 2. X - y = 0 (equation 2) x = 0 + y (express x in terms of y from equation 2) x = y (collect terms) 2x + 2x = 8 (substitute value of y) 4x = 8 (collect terms) 4x/4 = 8/4 (divide by 4) x = 2 We know that x = y, so y = 2.__Check:__2x + 2y = 8 (equation 1) 2(2) + 2(2) = 8 (substitute values) 4 + 4 = 8 (simplify) 8 = 8 (collect terms; correct!) x - y = 0 (equation 2) 2 - 2 = 0 (substitue values) 0 = 0 (collect terms; correct!)