a) 2x+3y=14 - > 2x = 14 -3y / :2 3x-2y=8 x = 7-³/₂y 3 (7-³/₂y) - 2y = 8 x= 7-³/₂y 21- ⁹/₂ y -2y = 8 x = 7-³/₂y -6½ y = 8-21 x= 7-³/₂y -¹³/₂ y = -13 / *(-²/₁₃) x=7-³/₂y y = 2 x=7-³/₂ *2 y=2 x=7-3 y=2 x=4 y=2 b) ½x-2y=8 -> ½x = 8 +2y / *2 2x+5y=6 x = 16+4y 2* (16+4y) +5 y = 6 x = 16+4y 32+8y+5y = 6 x =16+4y 13y = 6-32 x=16+4y 13y = -26 / : 13 x = 16+4y y = -2 x = 16 +4 * (-2) y=-2 x = 16-8 y = -2 x = 8 y = -2 c) ½x-¾y=0 -> ½x = ¾y / *2 ⅔x+1¼y=9 x = ³/₂ y ⅔ *³/₂ y +1¼y=9 x = ³/₂ y y +1¼y=9 x = ³/₂ y 2¼y=9 x = ³/₂ y ⁹/₄y=9 / * ⁴/₉ x = ³/₂ y y=4 x = ³/₂ *4 y=4 x = 6 y= 4 d) 3x+4y=1⅔ -> 3x = ⁵/₃ - 4y / :3 6x+3y=1¼ x = ⁵/₉ - ⁴/₃y 6 (⁵/₉ - ⁴/₃y) +3y=1¼ x = ⁵/₉ - ⁴/₃y ¹⁰/₃ - 8y +3y = ⁵/₄ x = ⁵/₉ - ⁴/₃y - 8y +3y = ⁵/₄ - ¹⁰/₃ x = ⁵/₉ - ⁴/₃y - 5y = -²⁵/₁₂ / : (-5) x = ⁵/₉ - ⁴/₃y y = -⁵/₁₂ x = ⁵/₉ - ⁴/₃ * (-⁵/₁₂) y = -⁵/₁₂ X =⁵/₉ + ⁵/₉ y = -⁵/₁₂ X = ¹⁰/₉ y = -⁵/₁₂ X = 1 ¹/₉ y = -⁵/₁₂
