Solve these simultaneously to find values for a and b: 6a + b = 16 and 5a - 2b = 19

In order to tackle questions like this with two letters of unknown value, first what we try to do is eliminate one of the variables completely from an equation. If we call 6a + b = 16 eqn 1 and 5a - 2b = 19 eqn 2, we can see that if we multiply both sides of eqn 1 by 2, and add eqn 2 to the new equation we get, we can get rid of the 'b' term, making the equation in terms of 'a' only. Doing this gives us the following: (12a +2b = 32) + (5a -2b = 19), which goes on to give 17a = 51, meaning a = 3. Substituting this value for 'a' back into one of the original equations will give us the answer for 'b'. Putting a = 3 into eqn 1 gives: (6 x 3) + b = 16, which goes on to give 18 + b = 16, meaning b = -2.