Given the equations: x + 3y = 1 and 2x - y = -5, solve for x and y.

Here we have 2 simultaneous equations including the variables x and y. Because we have x in one equation and 2x in another we can approach this in 2 ways. The first method is to obtain 2x in both equations so that we can equate and solve for y. If we multiply the equation x + 3y = 1 by 2 we get: 2x +6y = 2. With this we can now equate the simultaneous equations to get 2 - 6y = -5 + y, where we now only have the variable y which we can calculate as being equal to 1. With this information we can now sub y = 1 into the equation x + 3y = 1, which we solve to get x = -2. Therefore, we have solved the simultaneous equations and got x = -2 and y = 1, (we can check the results by plugging the values into the initial equations to make sure they work)