{{plz }} use algebraic rules of equations to predict the solution to the system of equations. include all of your work for full credit.
{x+2y=10
{6y=-3x+30

Step-by-step explanation:

The given system of equations is

First, we need to rewrite the system in order

Now, we multiply the first equation by -3, and solve

This means the system of equation has infinite number of solutions, that is, it's a consistent system.

The reason of this result is because both equation represent the same line, it's like one line is on top of the other, sharing all points, that's why it has infinte solutions.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.