Solve the equations x-y=1 and 5x-3y=13

These equations are what we call 'simultaneous' which means they are solved together. To do this, we need to make one of the variables (x or y) the subject of either of the equations.Rearranging the first equation to make x the subject gives,x=1+y. This can then be substituted into the other equation, leaving an equation with only one variable, 5(1+y)-3y=13. This means that it can be simply solved through re-arrangement! Simplification gives 5+5y-3y=13, 5-2y=13, -2y=-8, y=4. Finally, this y value can be subbed into either of the original 2 equations to give x. Subbing it into the first equation gives x=1+y, x=1+4=5