which represents the solution(s) of the system of equations, $y + 4 = x^{2}$ and $y - x = 2$? determine the…

which represents the solution(s) of the system of equations, $y + 4 = x^{2}$ and $y - x = 2$? determine the solution set by graphing.\n(-2, 0)\n(-2, 0) and (2, 0)\n(-2, 0) and (3, 5)\nno solutions

which represents the solution(s) of the system of equations, $y + 4 = x^{2}$ and $y - x = 2$? determine the solution set by graphing.\n(-2, 0)\n(-2, 0) and (2, 0)\n(-2, 0) and (3, 5)\nno solutions

Answer

Explanation:

Step1: Rewrite the second - equation

From $y - x=2$, we can get $y=x + 2$.

Step2: Substitute $y$ into the first equation

Substitute $y=x + 2$ into $y + 4=x^{2}$, we have $(x + 2)+4=x^{2}$, which simplifies to $x^{2}-x - 6=0$.

Step3: Factor the quadratic equation

Factor $x^{2}-x - 6=0$ as $(x + 2)(x - 3)=0$.

Step4: Solve for $x$

Set each factor equal to zero: $x+2 = 0$ gives $x=-2$; $x - 3=0$ gives $x = 3$.

Step5: Solve for $y$

When $x=-2$, $y=x + 2=-2 + 2=0$. When $x = 3$, $y=x + 2=3+2=5$.

Answer:

$(-2,0)$ and $(3,5)$