text: 2x - y + 2z = 15- - - - - -Equation 1\n-x + y + z = 3- - - - - - - Equation 2\n3x - y + 2z = 18- - -- -  - Equation 3\n- - - - - - - - - - - -\n\nElimination of y Equation 1 and equation 2\n\n2x - y + 2z = 15\n-x + y + z = 3\n- - - - - - - - - - -\nx + 3z = 18 . . Equation 4\n\n- - - - - - - - - - - - - -\nMultiply equation 3 by - 1\n\n3x - y + 2z = 18\n- 1(3x) - 1(-y) + (- 1)(2z) = - 1(18)\n-3x + y - 2z = - 18. . .New equation 3\n\n-- - - - - - - - - - - - - - -\n\nElimination of y and z equation 1 and new equation 3\n\n2x - y + 2z = 15\n-3x + y - 2z = - 18\n- - - - - - - - - - - -\n\n- x = - 3\n\n-1x = -3/-1\n\nx = 3\n\nThe answer is x = 3\n\nInsert the x value into equation 4\n\n- - - - - - - - - - - - - -\n\nSolving for z\n\nx + 3z = 18\n\n3 + 3z = 18\n\n3 + 3x - 3 = 18 - 3\n\n3z = 15\n\n3z/3 = 15/3\n\nz = 5\n\nThe answer is z = 5\n\nInsert the z value into equation 1\n\n- - - - - - - - - - - - - - - - - - - - - -\n\nSolving for y Equation 1\n\n2x - y + 2z = 15\n\n2(3) -y  + 2(5) = 15\n\n6 - y + 10 = 15\n\n16 - y = 15\n\n16 - y - 16 = 15 - 16\n\n- y = - 1\n\n- 1y = - 1\n\n-1y/-1 = - 1/- 1\n\ny = 1\n\nThe answer is y = 1\n\nInsert the y value into equation 1\n\n- - - - - - - - - - - - - - - - - - - - - -\n\nCheck for equation 1\n\n2x - y + 2z = 15\n\n2(3) - 1 + 2(5) = 15\n\n6 - 1 + 10 = 15\n\n5 + 10 = 15\n\n15 = 15\n\n- - - - - - - - - - - - - - - -\n\nCheck for equation 2\n\n- x + y + z = 3\n\n- 3 + 1 + 5 = 3\n\n-2 + 5 = 3\n\n3 = 3\n\n- - - - - - - - - - - - - \n\nCheck for equation 3\n\n3x - y + 2z = 18\n\n3(3) - 1 + 2(5) = 18\n\n9 - 1 + 10\n\n8 + 10 = 18\n\n18 = 18\n\n- - - - - - - - - - - - - - -\n\nThe solution set is { 3, 1, 5 }\n\n- - - - - - - -s-