Solve the following system of linear equations by graphing. (If the system has no solution, enter NONE for each answer. If the system is dependent, enter INFINITELY MANY for each answer.)

7x+2y=0
2x-7y=0

x =
y =

The determinant of the left-hand side is

|7 2 |
|2 -7|
=-49-4
=-53
which is non-zero. This implies that the system is not dependent.

So apart from the trivial solution of x=0 and y=0, there is no non-trivial solution.

To solve the system of linear equations by graphing, we will plot the graphs of both equations on the same coordinate plane and find the intersection point.

Start by rearranging both equations in slope-intercept form (y = mx + b).

Equation 1: 7x + 2y = 0
2y = -7x
y = (-7/2)x

Equation 2: 2x - 7y = 0
-7y = -2x
y = (2/7)x

Now let's graph both equations:

1. Equation 1 (y = (-7/2)x):
Choose several x-values, substitute them into the equation, calculate the corresponding y-values, and plot the points on the graph.
For example, when x = 0, y = (-7/2)*0 = 0.
When x = 2, y = (-7/2)*2 = -7. Plot the point (2, -7).
Repeat this process for other x-values and connect the points on the graph.

2. Equation 2 (y = (2/7)x):
Follow the same process as above by choosing different x-values, substituting them into the equation, and calculating the y-values. Plot the points and connect them on the graph.

The two lines will intersect at a particular point. The coordinates of this intersection point represent the solution to the system of equations.

Now, identify the coordinates of the intersection point, or determine if the lines are parallel or coincide with each other.

Upon solving this system of equations by graphing, you will find that the lines are coincident, meaning they are the same line. In this case, there are infinitely many solutions to the system.

Therefore, for both x and y, the answer is INFINITELY MANY.