Question 934439
It seems like the paper has to be
either graph paper somehow having squares measuring 2 cm,
or plain paper without lines.
 
One interpretation of the {{{-2<x<5}}} would be
that you have to show the graph of {{{y=2x+1}}} from point (-2,-3) to point (5,11) ,
but that would make the graph 28 cm tall.
 
The {{{-2<x<5}}} must just mean that your scale on the x-axis should go from -2 to 5.
There is no instruction for the y-axis scale,
but -2 to 5 works well too (see below).
{{{graph(300,300,-2,5,-2,5,2x+1,x/3-2/3)}}}
Since the scale is 2 cm to 1 unit,
the distance between marks on each axis would be 2 cm,
and the graph above would measure 14 cm by 14 cm.
To plot each line you would need 2 points, or a point and the slope.
{{{y=2x+1}}} is an equation in slope-intercept form,
which makes it clear that the line has a slope of {{{2}}} ,
and a y-intercept of {{{1}}} , so (0,1) is one point,
and for every 1 unit increase in x, y increases by 2,
so with those increases, from (0,1) we get to (1,3),
and then to (2,5).
To graph {{{y=2x+1}}} , you could plot points (0,1) and (2,5),
and draw the line that passes through them.
{{{x-3y=2}}} is given in standard form,
so graphing it is not that easy.
You notice that for {{{y=0}}} {{{x=2}}} ,
so the line passes through (2,0).
The slope is {{{1/3}}} ,
so for every 3 units increase in x,
there is a 1 unit increase in y.
Using those increments, staring from (2,0), we get to (5,1),
so to graph {{{x-3y=2}}}you could points (2,0) and (5,1),
and draw the line that passes through them.
The lines seem to intersect at (-1,-1),
If you substitute {{{x=-1}}} and {{{x=-1}}} into the equations of both lines,
it makes the equations true.
That means that point (-1,-1) belongs to both lines,
so it is the intersection point,
and the solution to the system of equations
{{{system(y=2x+1,x-3y=2)}}} ,
which you have solved by graphing.
That was the point of the exercise.
Without the request to graph for {{{-2<x<5}}},
you could have made this graph:
{{{graph(300,300,-0.5,9.5,-0.5,9.5,2x+1,x/3-2/3)}}} ,
which does not show the intersection point.