Let y represent the units digit. Let x represent the tens digit. Formulate Equations: 1. x = 3y (the tens digit is 3 times the unit digit) 2. 10y + x = 10x + y + 36 (if the digits are reversed, the new number will be 36 less thant the orginal number) Simplify Equations: Equation 1: X = 3y x - 3y = 3y - 3y (subtract 3y) x - 3y = 0 Equation 2: 10y + x = 10x + y + 36 10y - y + x - 10x = 10x - 10x + y - y + 36 (subtract y; subtract 10x) 9y - 9x = 36 (collect terms) 9y/9 - 9x/9 = 36/9 (divide each term by 9) y - x = 4 (simplify) Gaussian Elmination (x - 3y) + (y - x) = (4 + 0) (add equation 1 and 2 together) -2y = 4 (collect terms) -2y/-2 = 4/-2 (divide by -2) y = -2 (simplify) x = -2 * 3 x = -6 The number you seek will be: (-6 * 10) + (-2) = -62
