Solve the following simultaneous equations: 6a + b = 16; 5a - 2b = 19

There are 2 methods in solving this set of equations, in order to find the 2 unknowns: (a) and (b). Method 1: Firstly rearrange equation 1 to make (b) the subject: b = 16 - 6a. This can then be substituted into the (b) in equation 2 so the resulting equation only has 1 unknown, (a). 5a - 2(16 - 6a) = 19. Open up the brackets: 5a - 32 + 12a = 19, and then simplify the equation: 17a = 51. This equation can then be solved to get the value of (a): a=3. (a) can then be substituted into one of the equations to find (b): b = 16 - 6(3); b = -2Method 2: The aim of this method is to make one of the unknowns, (a) or (b), in both equations equal. For example, equation 1 can be multiplied by 2 to get 12a + 2b = 32. The 2 equations can then be added to each other in order to cancel out the (b)'s and obtain an equation with only 1 unknown. This equation can then be solved to get the value of (a). (12a + 2b) + (5a - 2b) = 32 + 19; 17a = 51; a = 3. The value of (a) can then be substituted into one of the equations in order to obtain (b).