How do you solve the following simultaneous equations? Equation 1: 2x + 3y = 13 Equation 2: 3x - y = 3

There are various ways to solve simultaneous equations. The two easiest are by elimiation and by substitution. By Elimation When solving by elimination you want to ensure that you only have one variable (x or y) in the remaining equation. In order to do this you want to have the coefficient (number in front of the variable) equal for one of the variables across the two equations. This requires some manoevering. Equation 2: 3x - y = 3 -3Equation 2 = -9x + 3y = -9 Then you are able to subtract one from the other Equation 1 --3Equation 2 = Equation 1 + 3Equation 2 = 2x + 3y = 13   + 9x - 3y = 9 = 11x = 22 x = 2 if x = 2, then 22 + 3y = 13 so 3y = 9 so y = 3 By Substitution This method means that one variable is rearranged to be the subject of one equation, then is substituted into the other, like seen below. Equation 2: 3x - y = 3 3x = y + 3 y = 3x - 3 Equation 1: 2x + 3y = 13 2x + 3(3x - 3) = 13 2x + 9x - 9 = 13 11x = 22 so x = 2 if x = 2, then 2*2 + 3y = 13 so 3y = 9 so y = 3