Respuesta :
Given the system of equations:
• y = x² - 4
,• y = -2x - 5
Let's find the solution(s) to the system.
To find the solution, eliminate the equivalent sides and equate the expressions.
We have:
[tex]x^2-4=-2x-5[/tex]Move all terms to the left and equate to zero.
Add 2x and 5 to both sides:
[tex]\begin{gathered} x^2+2x-4+5=-2x+2x-5+5 \\ \\ x^2+2x+1=0 \end{gathered}[/tex]Factor the left side of the equation using the perfect square rule:
[tex]\begin{gathered} x^2+2x+1^2=0 \\ \\ x^2+2\cdot x\cdot1+1^2=0 \\ \\ (x+1)^2=0 \end{gathered}[/tex]Solving further:
[tex]x+1=0[/tex]Subtract 1 from both sides:
[tex]\begin{gathered} x+1-1=0-1 \\ \\ x=-1 \end{gathered}[/tex]Now, substitute -1 for x in either of the equations and solve for y.
Let's take the first equation:
[tex]\begin{gathered} y=x^2-4 \\ \\ y=-1^2-4 \\ \\ y=1-4 \\ \\ y=-3 \end{gathered}[/tex]Therefore, we have the solutions:
x = -1, y = -3
In point form:
(x, y) ==> (-1, -3)
ANSWER:
A. (-1, -3)
