Solve the system of equations by graphing. Then classify the system.

2x-y=7
2x+3y=3

Graph them. See where they intersect, if they do so.

To solve this system of equations by graphing, follow these steps:

1. Graph the first equation, 2x-y=7:
a. To graph this equation, convert it into slope-intercept form by isolating y:
2x - y = 7
-y = -2x + 7
y = 2x - 7
b. Now you have a linear equation in the form y = mx + b, where m = 2 (the slope) and b = -7 (the y-intercept).
c. Plot the y-intercept at (0, -7) and use the slope to find additional points on the line. For example, if you move one unit to the right (x = 1), you will move two units up (y = -5). Connect these points to create a straight line.

2. Graph the second equation, 2x+3y=3:
a. Convert this equation into slope-intercept form as well:
2x + 3y = 3
3y = -2x + 3
y = (-2/3)x + 1
b. The slope is -2/3, and the y-intercept is 1. Plot these two points and draw a line through them.

3. Now, look at the graph and identify the point(s) where the two lines intersect. This point represents the solution to the system of equations.

4. If the lines intersect at a single point, the system of equations is consistent and has a unique solution. In this case, the system is classified as consistent and independent.

Alternatively, if the lines are parallel and do not intersect, there is no common solution, and the system is inconsistent. If the lines coincide, meaning they are on top of each other and intersect at infinite points, the system is consistent and dependent.

Please note that the precision of graphing by hand might not lead to exact solutions, so another method such as substitution or elimination is typically used to find the precise solution.