Solve the following simultaneous equations: 3a + 2b = 36 equation ( 1), and 5a + 4b = 64 equation (2)

This question can be answered by the elimination method, substitution method or graphically. I find the elimination method easiest, especially when you can see that the coefficient of a variable (in this case b) in one equation is a factor of the coefficient of that variable in the other equation. I will choose to eliminate 'b' in this case.

Firstly, multiply the whole of equation (1) by 2, resulting in 6a+4b=72. Now we can subtract equation (2): 5a+4b=64 from the new equation (1): 6a+4b=72. This results in a=8, showing we have eliminated 'b'. Fortunately this already gives us the answer for a. Next, substitute a=8 into any of the two equations. Let's choose equation (1): 3 x 8 + 2b =36, which leads to 2b = 12 , which leads to b=6. This means the answer is a=8 and b=6. To check our answer is correct, substitute these values for x and y into equation (2): 5 x 8 + 4 x 6 = 64, which gives 64 = 64, showing us that our answer is correct.