Select the correct answer.Solve the system of equations.y = -2x + 5y = x2 + 3x + 9A. (1,3) and (4,13)B. (-1,13) and (-4,7)C. (-1,7) and (-4,13)D. (-1,-3) and (-4,3)

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)