solve each of the following systems by graphing?

Question

17) 3x-2y=6
2x-y=5

Answer 1

All nonparallel, coplanar lines will intersect somewhere - the point they intersect is the one point (x, y) that they have in common and will satisfy both equations. So in graphing these two lines, you'll find your solution.

Graphing is easiest if you get your equations in slope-intercept form - make them say y = something. For the first one,

3x - 2y = 6
2y = 3x - 6
y = 3x/2 - 3

And the second one:

2x - y = 5
y = 2x - 5

Graphing is easy - start with the y-intercept and count off your slope. For the first one, your y-intercept is -3 and your slope is 3/2 - up 3 places and over to the right 2 places. You can do that a few times, and when you're done, just connect the dots. The same goes for the second equation - start at -5 and go up 2 and over to the right 1 (the slope is 2, which fractionally is 2/1).

If you draw your graph correctly, the two should intersect at (4, 3). You can check this by plugging in 4 for the x in both equations, and you should get y = 3 both times.