Answer:
Option C. The solution for the system of equations is (-1,7) and (-4,13)
Solution:
The equation for the system given is,
[tex]y = -2x + 5[/tex]
[tex]y=x^{2}+3 x+9[/tex]
Now we can write,
[tex]-2 x+5=x^{2}+3 x+9[/tex]
[tex]x^{2}+3 x+9+2 x-5=0[/tex]
[tex]x^{2}+5 x+4=0[/tex]
[tex]x^{2}+4 x+x+4=0[/tex] (//simplifying)
[tex]x(x+4) +1(x+4) = 0[/tex]
[tex](x+4)(x+1) = 0[/tex]
[tex]x = -4 \ or -1[/tex]
When [tex]x = -4, \ then \ y = -2\times(-4) + 5 =13[/tex]
When [tex]x = -1, \ then \ y = -2\times(-1)+5 = 7[/tex]
So, solution is C, (-4,13) and (-1,7)
