How can graphs be used in solving equations?

The first thing that is important to understand that a graph essentially highlights every single possible value (for both x and y) within a given rangeWhat does this mean?This means that a line representing y=x+2 will represent every single value of x corresponding to every single possible value of y,Now if I were to give you the following problem:The price of a chocolate and a biscuit is £6 and that the cost of a biscuit is half the price of a chocolate.Now lets break this down:If the price of a chocolate is represented by x and the price of a biscuit is y Thenx+y=6and x/2=y or x=2yNow this can be solved quite easily by substituting the second equation into the first, but lets use a graph instead,First plot x+y=6, in order to plot this graph you must make it in terms of y, so y=6-xSo the points will be as followsy x1 52 43 3
and so on...Then x=2y y x1 22 43 6
Now with both graphs plotted, we find that they intersect at the point (4,2)Meaning the values of x and y are 4 and 2 respectively.