Solve the simultaneous equations 2a + b =4 and 5a – 3b = -1

When you solve normal equations like 4x-2=7, there is one equation and one unknown value. This case is no different: in order to solve these equations, you need to create one equation with one unknown. We start by labelling the equations 1 and 2. This method is called the substitution method. First we have to rewrite one of the equations, isolating one of the variables on one side. In this example, this is easiest with equation 1 (2a + b =4 --> b = 4 - 2a). We now have an expression for b, which we can substitute into equation 2. This gives 5a - 3(4 - 2a) = -1. We can then solve this new equation to give us 11a = 11, a = 1. We can then use a = 1 to find b, by substituting this value into one of the original equations. Using equation 1, we get 2(1) + b = 4, so b = 2, and a = 1.