Question

69 points!!!

Answer 1

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 : $x^{2} + y^{2} = 25\\2x + y = -5$

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

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

We get: $x^{2} + y^{2} = 25 \implies x^{2} + (-5-2x)^{2} = 25$

By ALGEBRAIC IDENTITY:

$(a+b)^{2} = a^{2} + b^{2} + 2ab\\ (-5-2x)^{2} = (-5)^{2} + (-2x)^{2} + 2(-5)(-2x)$

or, $x^{2} + (-5-2x)^{2} = 25 \implies x^{2} + (25 + 4x^{2} + 20x) = 25$

or, $5x^{2} + 20x = 0 \implies x(5x + 20) = 0$

⇒ 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)