When an equation in first degree is given in the form y=mx+b then this can immediately be graphed with a slope of m and y intercept of b. A first degree equation is an equation that does not contain any variables raised to second power or greater.
The given equation is x+y=3. Subtract x from both sides. This will result in the equation below:
Rearranging the right side we can write the above equation as
This equation is of the form y=mx+b (with m=-1 and b=3)
To graph this line, mark the first point at 3 on the y axis (b is 3 from above)
Since m, which is the slope, is -1, mark another point relative to this first point 1 unit to left and 1 unit up. We do this because the slope is -1 and a slope of -1 means 1 unit rise for -1 unit for run.
Join the two plotted points and extend in both ends to get the required line on the graph.
Do similar operations on x-y=5 as I explained for x+y=3. Perform operations on the given equation so that the equation transforms to y=mx+b form as follows:
subtracting y and 5 from both sides we get
x-5 = y or y=x-5
This can also be written as y=1*x-5
This is now in the form y=mx+b where m=1 and b=-5
Now mark the point -5 on the y axis. Mark another point 1 unit to the right and 1 unit up from this first point.
Join the two points and extend in both directions to get the required graph
The line for x+y=3 and x-y=5 will intersect at some point. Note the x and y coordinates at this point of intersection. This is the ordered pair for the required solution.