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

Question

asked Aug 10, 2020 233k views

2 Answers

Sinh Nguyen · Answer 1 · 2020-08-14T05:07:59+0000

Answer:

Option C. The solution for the system of equations is (-1,7) and (-4,13)

Solution:

The equation for the system given is,

y = -2x + 5

y=x^(2)+3 x+9

Now we can write,

-2 x+5=x^(2)+3 x+9

x^(2)+3 x+9+2 x-5=0

x^(2)+5 x+4=0

x^(2)+4 x+x+4=0 (//simplifying)

x(x+4) +1(x+4) = 0

(x+4)(x+1) = 0

$x = -4 \ or -1$

When
$x = -4, \ then \ y = -2*(-4) + 5 =13$

When
$x = -1, \ then \ y = -2*(-1)+5 = 7$

So, solution is C, (-4,13) and (-1,7)