Solve the following simultaenous equations

6a + 3b = 7 (1) 4a + 4b = 12 (2) We need to eliminate one of the variables in our simultaneous equations in order to be able to find a numerical value. As the same signs are used in both equations (i.e. addition), this could be achieved by subtracting one equation from the other, once one of the variables are equated (thus removing this variable). For example: (1) x 4 gives 24a + 12b = 28 (2) x 3 gives 12a + 12b = 36 Thus the b variable is equal in both equations and if we now subtract (2) from (1) we have an equation in a: 12a = -8 and solving gives a = -2/3. Substitute a back into our original (1): (6 x -2/3) + 3b = 7 3b - 4 = 7 b = 11/3 Check in original (2): (4 x -2/3) + (4 x 11/3) = -8/3 + 44/3 = 12 (as this is equal to (2) the values for a and b are correct)