1. X2 + y2 = 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) x2 + x2 = 8 (substitute value of y into equation 1) x4 = 8 (apply exponent law) (x4)(1/4) = 8(1/4) (eliminate the exponent) x = 2 (simplify) We know that x = y. This concludes that y = 2. Check: x2 + y2 = 8 (eqaution 1) 22 + 22 = 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!)
