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)

step-by-step explanation:

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point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.