Question 887699
To graph a line all you need is two points on that line.  You can either pick points and plug them into the equations given or, and this is how I will do it, you can get both equations into slope intercept form which will give you the two points you need to graph each line.<br>

So first we need to solve each equation for y to get it into slope intercept form.<br>

-x+3y = 8 add x to both sides
3y = 8+x divide both sides by 3
y = 8/3 + 1/3x<br>

x+y=2 subtract x from both sides
y = 2-x<br>

Now that we have both equations in slope intercept form we can look at each equation individually.  {{{y=8/3+(1/3)x}}} tells us that the y intercept is 8/3 and the slope is 1/3.  So we know that the graph goes through the point (0,8/3) from the y-intercept.  And remembering that slope is the change in y over the change in x we know that the graph then goes up one and over 3.  So our new point would be (0+3,8/3+1) or (3,11/3).  You can plot these two points and then connect the points with the line.<br>

Next we look at {{{y = 2-x}}}.  The y intercept is 2 and the slope is -1.  So we know that the graph goes through the point (0,2) from the y-intercept.  Moving down 1 and over 1 puts our next point at (0+1,2-1) or (1,1).  Plotting these two points will yield your line.<br>

To finish this problem you will look to see where the two lines intersect.  This will be your solution.  I will leave this for you to do.