Solving a Three Variable System of Equations

Here is the problem from class: a + b + c = 5, 2a + 3b + c = 10, 4a - b + c = 9. So, solve for c in the first equation. c = 5 - a - b. So, substitute the equation of c into the other equations. 2a + 3b + 5 - a - b = 10, 4a - b + 5 - a - b = 9. So, simplify the equations. a + 2b = 5, 3a - 2b = 4. So through elimination, add the equations. 4a = 9, therefore a = 2.5. So let's use two equations: a + b + c = 5, 4a - b + c = 9. So through elimination, add the equations. 5a + 2c = 14, and since a = 2.5, 5(2.5) + 2c = 14, 12.5 + 2c = 14, 2c = 1.5 and therefore, c = .75. So, a + b + c = 5 with the values of a and c, look like: 2.5 + b + .75 = 5. Solve for b. b = 1.75. Check your work and the values add up to 5.