Solve the simultaneous equations: 3x-y=13, 2x+y=12

To solve these simultaneous equations we first need to eliminate one variable (the x or the y). For this we will need the coefficients (numbers in front of the variables) to be equal or opposite on one variable in each of the equations. In our question, we can already see the first equation has a +1 in front of the y, and the second equation has a -1 in front of the y. Adding these two equations together gets 5x=25 which is great because the y has been completely eliminated and we can divide both sides of the equation by 5 to get x=5! Substituting this back into our first equation gives (2x5)+y=12. Take 10 off both sides to get y=2, and there we have solved the simultaneous equations for x and y.