Respuesta :
You have a system of equations [tex] \left \{ {{y = -x^2+2x-9} \atop {y =-6x+6}} \right. [/tex].
1. Substitude right side of second equation into the left side of the first equation: [tex]-6x+6=-x^2+2x-9[/tex].
2. Solve this equation:
[tex]x^2-2x+9-6x+6=0, \\ x^2-8x+15=0, \\ D=(-8)^2-4\cdot 1\cdot 15=64-60=4, \\ \sqrt{D}=2, \\ x_{1,2}=\dfrac{8\pm 2}{2 } =3,5[/tex].
3. Find y:
for [tex]x_1=3, y_1=-6\cdot 3+6=-18+6=-12[/tex],
for [tex]x_2=5, y_2=-6\cdot 5+6=-30+6=-24[/tex].
4. The solutions of the system are: (3,-12) and (5,-24).
Answer: Correct choice is A.
1. Substitude right side of second equation into the left side of the first equation: [tex]-6x+6=-x^2+2x-9[/tex].
2. Solve this equation:
[tex]x^2-2x+9-6x+6=0, \\ x^2-8x+15=0, \\ D=(-8)^2-4\cdot 1\cdot 15=64-60=4, \\ \sqrt{D}=2, \\ x_{1,2}=\dfrac{8\pm 2}{2 } =3,5[/tex].
3. Find y:
for [tex]x_1=3, y_1=-6\cdot 3+6=-18+6=-12[/tex],
for [tex]x_2=5, y_2=-6\cdot 5+6=-30+6=-24[/tex].
4. The solutions of the system are: (3,-12) and (5,-24).
Answer: Correct choice is A.