69 points!!!What are the solutions of the following system?{x² + y² = 25{ 2x+y=-5A(0,-5) and (-5,5)B (0,-5) and (5, -15)C(0, -5) and (-4,3)D(0,-5) and (4, -13)

Answer: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 : [tex]x^{2}  + y^{2}  = 25\\2x  + y  = -5[/tex]from equation 2, we get   y = -5 - 2x .Put the above value of y in the equation (1).We get: [tex]x^{2}  + y^{2}  = 25  \implies x^{2}  + (-5-2x)^{2}  = 25[/tex]By ALGEBRAIC IDENTITY:[tex](a+b)^{2}   = a^{2}  +  b^{2}  + 2ab\\ (-5-2x)^{2} = (-5)^{2}  +  (-2x)^{2}  + 2(-5)(-2x)[/tex]or, [tex]x^{2}  + (-5-2x)^{2}  = 25  \implies x^{2} + (25  +  4x^{2}  + 20x)  = 25[/tex]or, [tex]5x^{2}  + 20x = 0  \implies x(5x + 20) = 0[/tex]⇒ x = 0 or,   x  = -20/5 = -4So, the possible values for x are: x  = 0 or  x  = -4If x  = 0, y = -5-2x = -5-2(0) = -5and if x = -4, y = -5 -2(-4)   = -5 + 8  = 3Hence, the solution for the given system of equations are A(0,-5) and B(-4,3)