69 !

what are the solutions of the following system?
{x² + y² = 25
{ 2x+y=-5

a(0,-5) and (-5,5)
b (0,-5) and (5, -15)
c(0, -5) and (-4,3)
d(0,-5) and (4, -13)

C)  The solution for the given system of equations are A(0,-5) and B(-4,3)

Step-by-step explanation:

The given system of equation are :

from equation 2, we get   y = -5 - 2x .

Put the above value of y in the equation (1).

We get:

By ALGEBRAIC IDENTITY:

or,

or,

⇒ x = 0 or,   x  = -20/5 = -4

So, the possible values for x are: x  = 0 or  x  = -4

If x  = 0, y = -5-2x = -5-2(0) = -5

and if x = -4, y = -5 -2(-4)   = -5 + 8  = 3

Hence, the solution for the given system of equations are A(0,-5) and B(-4,3)

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'.

step-by-step explanation: