Question

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)

Answer 1

a

Explanation:

Answer 2

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)