Posted by Dean on Saturday, July 12, 2008 at 1:27pm.
Draw a graph showing the two straight lines defined by those equations. They will intersect at a point (x,y), and that is the solution.
X-Y = 0 is a 45 degree line (slope = 1) through the origin. The other line has a slope of -1 and passes through the point (0,2).
Pick any two points on each of the equations.
For your equations that should be quite easy, you should be able to do so by just inspection.
e.g. for the first one (2,0) and (0,2) would work, I used the intercepts.
Join these two points and draw a straight line.
for the second one, how about (0,0) and (5,5) ?
Join these two points and draw a straight line.
Where these two lines intersect becomes the solution to the system.
(looks like (1,1) is the intersection point)
Some calculators are graphing calculators but I don't know how to use them. If you have one, read the instructions. For doing this manually,
make a table with two columns. The dots are to control spacing; they have no meaning mathematically.
X......Y
Using the first equation, let X = 0 and solve for Y. Y= 2 so write 0 in the X column and 2 in the Y column. Then give X a value of 1 and solve for Y. Y = 1. Place 1 in the X column and 1 in the Y column. Technically you can quit here since two points define a straight line; however, I often make little arithmetic errors so I usually plot a third point to make sure it is on the same line. So I usually give Y = 0 and solve for X. X = 2. Now plot those three points on a sheet of graph paper and draw the line.
Do the same thing for the second equation and plot those points on the same sheet and draw the line. The solution of the set of equation is where the two straight lines intersect. If I didn't goof, they should intersect at X=1, Y = 1 but check my work.