A quick and dirty way to graph the systems in (1) and (2) would be to find the x and y intercepts and plot them.
To find the x-intercept of each equation, set y = 0 and solve for x
To find the y-intercept of each equation, set x = 0 and solve for y
This will give you two ordered pairs for each linear equation. You can plot them, and draw a straight line between them. The lines should intersect in your first set, since the slopes are different. Try to determine where that intersection is by looking at your graph. It should be fairly easy since the ordered pair of the intersection is made up of integers.
The second set is a bit different. The slopes are the same. What do you know about lines that have the same slope. Do they intersect?
Finally, your last set of 3 linear equations. y = x is a line of slope 1 that bisects the 1st and 3rd quadrants. y = 0 is actually the x-axis, itself. And, 2x + 3y = 10 is a line that has an x-intercept at (5, 0) and a y-intercept at (0, 10/3). Looking at the graph, one vertex is obviouslly at (0, 0). Another is at the x- intercept of 2x + 3y = 10 which is (5, 0). The third vertex if found by solving the system:
(1) 2x + 3y = 10
(2) y = x
Substitute x for y in (1): 2x +3x = 10
5x = 10
x = 2
If x = 2, then so does y, since y = x
Therefore, the third vertex is (2, 2)
Your 2 vertices are (0. 0), (5, 0), (2, 2).
I didn't know how much detail you needed, but I hope this helps.
