Question 82692
Simply graph {{{y=-x+3}}} and {{{y=x+1}}} on one graph like this


{{{ graph( 300, 200, -5, 5, -5, 5, -x+3, x+1) }}} graph of {{{y=-x+3}}} (red) and {{{y=x+1}}}(green)


The solution to the system is the point of intersection. So it appears they intersect at (1,2). So the solution is (1,2).


If you aren't allowed to use a graphing calculator, then you must make a table for each equation. 


So if you let x=1 you get

{{{y=-(1)+3=2}}}

{{{y=2}}}

and you would do this for every point in your table


So the table for {{{y=-x+3}}} would look like

<pre>

          x          y
   -5.00000    8.00000
   -4.00000    7.00000
   -3.00000    6.00000
   -2.00000    5.00000
   -1.00000    4.00000
    0.00000    3.00000
    1.00000    2.00000
    2.00000    1.00000
    3.00000    0.00000
    4.00000   -1.00000
    5.00000   -2.00000

</pre>


Also, if you're required to make tables, you would have to make another table for {{{y=x+1}}}


After making the tables, you can simply plot them on graphing paper to see where they intersect. That intersection is the solution.